Graphene membrane with regular angstrom-scale pores

ABSTRACT

Technologies are generally described for perforated graphene monolayers and membranes containing perforated graphene monolayers. An example membrane may include a graphene monolayer having a plurality of discrete pores that may be chemically perforated into the graphene monolayer. The discrete pores may be of substantially uniform pore size. The pore size may be characterized by one or more carbon vacancy defects in the graphene monolayer. The graphene monolayer may have substantially uniform pore sizes throughout. In some examples, the membrane may include a permeable substrate that contacts the graphene monolayer and which may support the graphene monolayer. Such perforated graphene monolayers, and membranes comprising such perforated graphene monolayers may exhibit improved properties compared to conventional polymeric membranes for gas separations, e.g., greater selectivity, greater gas permeation rates, or the like.

CROSS-REFERENCE TO RELATED APPLICATIONS

This Application is the National Stage filing under 35 U.S.C §371 of PCTApplication Ser. No. PCT/US12/22798 filed on Jan. 26, 2012. The PCTApplication is herein incorporated by reference in its entirety.

BACKGROUND

Unless otherwise indicated herein, the materials described in thissection are not prior art to the claims in this application and are notadmitted to be prior art by inclusion in this section.

Porous graphene is considered to be a desirable membrane for gasseparation. Theoretical and experimental studies indicate thatatom-scale holes in the graphene lattice may provide significantselectivity for separating gases based on molecular size. Further,monolayer graphene, at one atom thick, is a desirable candidate becausethe gas permeation rate through a membrane increases with decreasingmembrane thickness.

Consequently, porous graphene membranes are being pursued for theirpotential to significantly outperform conventional polymeric membranes,e.g., in separating gases that are synthesized at high temperatures. Forexample, the “shift reaction” used to create hydrogen gas from water andcarbon dioxide may run at temperatures over 400° C. Since there iscurrently no membrane that effectively purifies hydrogen in a singleoperation, much less at such high temperatures, current hydrogenpurification may include capital and energy intensive operations such ascooling, as well as removal of water, carbon dioxide, and otherimpurities.

A graphene membrane with uniformly sized pores may effectively purifyhydrogen from the “shift reaction” in a single operation. However,although porous graphene has shown interesting performance insmall-scale academic studies, current preparation methods are notcapable of preparing a graphene membrane with uniformly sized pores.Known porous graphene examples have been created using a physicalprocess such as electron or ion beams to damage the graphene surface,followed by oxidative expansion of the defects to create pores. Suchmethods have created porous graphene membranes with pores that varysignificantly in size and in areal density over the membrane.

The present disclosure appreciates that preparing porous graphene, e.g.,for use in separation membranes, may be a complex undertaking.

SUMMARY

The following summary is illustrative only and is not intended to be inany way limiting. In addition to the illustrative aspects, embodiments,and features described above, further aspects, embodiments, and featureswill become apparent by reference to the drawings and the followingdetailed description.

The present disclosure generally describes perforated graphenemonolayers, and membranes that include perforated graphene monolayers.An example membrane may include a graphene monolayer with a plurality ofdiscrete pores that are chemically perforated therein. Each of theplurality of discrete pores may have a substantially uniform pore sizecharacterized by one or more carbon vacancy defects in the graphenemonolayer such that the graphene monolayer may have substantiallyuniform pore sizes throughout.

The present disclosure also generally describes example methods offorming a plurality of discrete pores in a graphene monolayer. Anexample method may include contacting a compound represented by R-Het*to a plurality of locations at the graphene monolayer. Het* may benitrene or activated oxy. R may be one of —R^(a), —SO2R^(a),—(CO)OR^(a), or —SiR^(a)R^(b)R^(c). R^(a), R^(b), and R^(c) may beindependently aryl or heteroaryl. Some example methods may also includeproviding a separation distance of at least r_(R) between adjacentlocations in the plurality of locations, wherein r_(R) may be a minimumsteric radius of R. Various example methods may also include reactingthe compound represented by R-Het* with at least one graphene carbonatom C_(g) at each of the plurality of locations to form a plurality pof heteroatom-carbon moieties at the graphene monolayer represented by[R-Het-C_(g)]_(p)graphene. The method may also include forming aplurality of discrete pores in the graphene monolayer by removing aplurality of the heteroatom-carbon moieties represented by R-Het-C_(g),The plurality of discrete pores may be characterized by a plurality ofcarbon vacancy defects in the graphene monolayer defined by removing thegraphene carbon atoms C_(g) from the plurality of locations. Thegraphene monolayer may have substantially uniform pore sizes throughout.

The present disclosure also generally describes methods of separating acompound from a fluid mixture. An example method may include providing afluid mixture that contains a first compound and a second compound. Someexample methods may also include providing a membrane that includes agraphene monolayer that may be chemically perforated by a plurality ofdiscrete pores. Each of the plurality of discrete pores may becharacterized by one or more carbon vacancy defects such that thegraphene monolayer has substantially uniform pore sizes throughout. Eachof the plurality of discrete pores may be characterized by a diameterthat may be selective for passage of the first compound compared to thesecond compound. Various example methods may also include contacting thefluid mixture to a first surface of the graphene monolayer. Examplemethods may further include directing the first compound through theplurality of discrete pores to separate the first compound from thesecond compound.

The present disclosure also generally describes an example membrane. Theexample membrane may be prepared by a process that includes contacting acompound represented by R-Het* to a plurality of locations at a graphenemonolayer. Het* may be nitrene or activated oxy. R may be one of —R^(a),—SO2R^(a), —(CO)OR^(a), or —SiR^(a)R^(b)R^(c). R^(a), R^(b), and R^(c)may be independently aryl or heteroaryl. Some example membranes may beprepared by a process that also includes providing a separation distanceof at least r_(R) between adjacent locations in the plurality oflocations, wherein r_(R) may be a minimum steric radius of R. Theexample membrane may be prepared by a process that further includesreacting the compound represented by R-Het* with at least one graphenecarbon atom C_(g) at each of the plurality of locations to form aplurality p of heteroatom-carbon moieties at the graphene monolayerrepresented by [R-Het-C_(g)]_(p)graphene. The example membrane may beprepared by a process that also includes forming a plurality of discretepores in the graphene monolayer by removing a plurality of theheteroatom-carbon moieties represented by R-Het-C_(g). The plurality ofdiscrete pores may be characterized by a plurality of carbon vacancydefects in the graphene monolayer defined by removing the graphenecarbon atoms C_(g) from the plurality of locations. The graphenemonolayer may have substantially uniform pore sizes throughout.

The present disclosure also generally describes system for preparing agraphene membrane with substantially uniform pores. The system mayinclude: a reagent activator for preparing an activated reagent from aprecursor reagent; a reagent applicator configured to contact theactivated reagent to a plurality of locations at a graphene monolayer; areaction chamber configured to hold the graphene monolayer; a heaterconfigured to thermally cleave a plurality of heteroatom-carbon moietiesat the graphene monolayer to form a perforated graphene monolayer; and asupport substrate applicator configured to contact the perforatedgraphene monolayer to a support substrate.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features of this disclosure will become morefully apparent from the following description and appended claims, takenin conjunction with the accompanying drawings. Understanding that thesedrawings depict only several embodiments in accordance with thedisclosure and are, therefore, not to be considered limiting of itsscope, the disclosure will be described with additional specificity anddetail through use of the accompanying drawings, in which:

FIG. 1A is a conceptual drawing of an example graphene monolayer,illustrating the hexagonal lattice of carbon atoms and aromatic bondscharacteristic of graphene;

FIG. 1B is a conceptual drawing of example graphene monolayer, showingone graphene carbon atom to be removed from a plurality of locations;

FIG. 1C is a conceptual drawing of an example perforated graphenemonolayer, including a plurality of discrete pores which may have asubstantially uniform pore size characterized by one carbon vacancydefect per pore;

FIG. 1D is a conceptual drawing of an example graphene monolayer,showing graphene carbon atoms to be removed from each of a plurality oflocations;

FIG. 1E is a conceptual drawing of an example perforated graphenemonolayer, including a plurality of discrete pores which may have asubstantially uniform pore size characterized by two carbon vacancydefects per pore;

FIG. 2A is a conceptual drawing of a side view of an example membranethat includes an example perforated graphene monolayer in contact with apermeable substrate;

FIG. 2B is a conceptual drawing of a side view of an example membraneillustrating a method of separating a fluid mixture of two compounds;

FIG. 3A is a conceptual drawing showing a method of forming a pluralityof discrete pores in a graphene monolayer, including steric interactionsbetween adjacent reagents;

FIG. 3B is a conceptual drawing showing additional operations which maybe included in a method of forming a plurality of discrete pores in agraphene monolayer;

FIG. 4 depicts an example reaction scheme corresponding to the generalscheme shown in FIG. 3A and FIG. 3B;

FIG. 5A depicts an example reaction scheme where an example graphenemonolayer may be contacted with a plurality of substituted nitreneradicals;

FIG. 5B depicts an example reaction scheme which may be employed forforming pores containing single carbon vacancy defects from nitrenereagents;

FIG. 5C depicts an example reaction scheme which may be employed forforming pores containing double carbon vacancy defects from nitrenereagents;

FIG. 5D depicts an example reaction scheme which employs a 1,2 dietherto form a 1,2 diol intermediate compound in the course of forming porescontaining double carbon vacancy defects from activated oxy reagents;

FIG. 5E depicts an example reaction scheme which employs a 1,2 diestermoiety to form a 1,2 diol intermediate compound in the course of formingpores containing double carbon vacancy defects from activated oxyreagents;

FIG. 6 is a flow diagram showing operations that may be used in makingan example perforated graphene monolayer or a membrane thereof;

FIG. 7 is a block diagram of an automated machine 700 that may be usedfor making an example perforated graphene monolayer;

FIG. 8 illustrates a general purpose computing device that may be usedto control the automated machine of FIG. 7 in making an exampleperforated graphene monolayer or membrane thereof;

FIG. 9 illustrates a block diagram of an example computer programproduct that may be used to control the automated machine of FIG. 7 orsimilar manufacturing equipment in making an example perforated graphenemonolayer or example membrane thereof;

all arranged in accordance with at least some embodiments as describedherein.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings, which form a part hereof. In the drawings,similar symbols typically identify similar components, unless contextdictates otherwise. The illustrative embodiments described in thedetailed description, drawings, and claims are not meant to be limiting.Other embodiments may be utilized, and other changes may be made,without departing from the spirit or scope of the subject matterpresented herein. It will be readily understood that the aspects of thepresent disclosure, as generally described herein, and illustrated inthe Figures, can be arranged, substituted, combined, separated, anddesigned in a wide variety of different configurations, all of which areexplicitly contemplated herein.

This disclosure is generally drawn, inter alia, to compositions,methods, apparatus, systems, devices, and/or computer program productsrelated to manufacturing or using perforated graphene, for example aspart of membrane which may be used in gas separation.

Briefly stated, technologies are generally described for a membrane thatmay include a graphene monolayer having a plurality of discrete poresthat may be chemically perforated into the graphene monolayer. Thediscrete pores may be of substantially uniform pore size. The pore sizemay be characterized by one or more carbon vacancy defects in thegraphene monolayer. The graphene monolayer may have substantiallyuniform pore sizes throughout. In some examples, the membrane mayinclude a permeable substrate that contacts the graphene monolayer andwhich may support the graphene monolayer. Such perforated graphenemonolayers, and membranes comprising such perforated graphene monolayersmay exhibit improved properties compared to conventional polymericmembranes for gas separations, e.g., greater selectivity, greater gaspermeation rates, or the like.

FIG. 1A is a conceptual drawing of an example graphene monolayer 100.FIG. 1A illustrates the hexagonal lattice of carbon atoms and aromaticbonds characteristic of graphene. The placement of the carbon-carbondouble bonds in example graphene monolayers described herein, forexample, in monolayer 100, is intended to be illustrative of grapheneand is not intended to be limiting.

FIG. 1B is a conceptual drawing of example graphene monolayer 100,showing one graphene carbon atom 102 to be removed from a plurality oflocations in example graphene monolayer 100. Removal of graphene carbonatoms 102 forms example graphene monolayer 106 in FIG. 1C. FIG. 1B alsoshows a minimum steric separation 104 between adjacent locations inexample graphene monolayer 100. Minimum steric separation 104 may alsocorrespond to the diameter of a circle 105 around graphene carbon atom102. Circle 105 may correspond to a minimum steric radius r_(R) of an Rgroup in a bulky chemical perforation reagent R-Het*. Methods ofchemical perforation using bulky reagents R-Het* are described furtherin the discussion of FIGS. 4A-5E.

FIG. 1C is a conceptual drawing of an example perforated graphenemonolayer 106. A plurality of discrete pores 108 are chemicallyperforated in example graphene monolayer 106. Discrete pores 108 mayhave a substantially uniform pore size characterized by one or morecarbon vacancy defects in graphene monolayer 106. In various examples,each discrete pore 108 may include hydrogen-passivated carbon atoms 110.FIG. 1C also shows a minimum steric separation 104 between adjacentdiscrete pores 108. Minimum steric separation 104 may also correspond tothe diameter of circle 105 around discrete pores 108.

FIG. 1D is a conceptual drawing of an example graphene monolayer 112,showing graphene carbon atoms 114 and 116 to be removed from each of aplurality of locations in example graphene monolayer 112, leading toexample graphene monolayer 120 in FIG. 1E. FIG. 1D also shows a minimumsteric separation 118 between adjacent locations in example graphenemonolayer 112. Minimum steric separation 118 may also correspond to thediameter of a circle 119 around graphene carbon atoms 114 and 116.Circle 119 may correspond to a minimum steric radius r_(R) of an R groupin a bulky chemical perforation reagent R-Het*. Methods of chemicalperforation using bulky reagents R-Het* are described further in thediscussion of FIGS. 4A-5E.

FIG. 1E is a conceptual drawing of an example perforated graphenemonolayer 120. A plurality of discrete pores 122 are chemicallyperforated in example graphene monolayer 120. Each of the plurality ofdiscrete pores 122 may have a substantially uniform pore sizecharacterized by two or more carbon vacancy defects in graphenemonolayer 120. In various examples, each discrete pore 120 may includehydrogen-passivated carbon atoms 124. FIG. 1E also shows minimum stericseparation 118 between adjacent discrete pores 122. Minimum stericseparation 118 may also correspond to the diameter of circle 119 arounddiscrete pores 122.

As used herein, “graphene” generally means a planar allotrope of carboncharacterized by a hexagonal lattice of carbon atoms that may beconnected by aromatic carbon-carbon bonds, e.g., as illustrated bygraphene 100 in FIG. 1A. As used herein, a graphene “monolayer”generally may be a one-carbon atom thick layer of graphene. In someexamples, the graphene monolayer may include some nonaromatic carbons,e.g., some carbons may be passivated with hydrogen and may be bonded toother carbons by nonaromatic single carbon-carbon bonds. As used herein,a “perforated graphene monolayer” generally may refer to a graphenemonolayer that may include a plurality of discrete pores through thegraphene monolayer. The discrete pores may pass entirely through thegraphene monolayer. The discrete pores may permit selective passage ofatomic or molecular species from one side of the graphene monolayer tothe other side of the graphene monolayer. As used herein, a “chemicallyperforated” pore in the graphene may be characteristic of preparation byselective removal of one or more carbon atoms from the graphene lattice,for example, the perforation shown between FIGS. 1B and 1C, or theperforation shown between FIGS. 1D and 1E. For example, atomic ormolecular species may be reacted with the graphene in a process whichresults in selective removal of one or more carbon atoms from thegraphene lattice. Example procedures for preparing the pores aredescribed further in the discussion of FIGS. 3A-5E.

As used herein, “discrete” pores in a graphene monolayer are distinctfrom each other by at least one intervening carbon-carbon bond, or insome examples, at least one intervening six-membered graphene ring. Forexample, in FIG. 1C, discrete pores 108A and 108B are separated by atleast four six membered rings or at least five carbon-carbon bonds.Also, for example, in FIG. 1C, discrete pore 108C may be separated fromeach of discrete pores 108A and 108B by at least three six-memberedrings or at least four carbon-carbon bonds. In another example, in FIG.1E, discrete pores 122A and 122B are separated by at least four sixmembered rings or at least five carbon-carbon bonds. Also, for example,in FIG. 1E, discrete pore 122C may be separated from each of discretepores 122A and 122B by at least three six-membered rings or at leastfour carbon-carbon bonds.

As used herein, “minimum steric separation” generally may refer to thedistance between the centers of adjacent discrete pores, such asdistance 104 in FIG. 1C or distance 118 in FIG. 1E. For example, aminimum steric separation corresponding to at least one interveningcarbon-carbon bond may be at least about 1 angstrom. In some examples, aminimum steric separation corresponding to at least one interveningsix-membered graphene ring may be at least about 4 angstroms. In variousexamples, a minimum steric separation may range from between about 1angstrom to about 100 angstroms, for example, at least about 1, 2, 3, 4,5, 6, 7, 8, 9, 10, 12.5, 15, 20, 25, 35, or 50 angstroms. As usedherein, “minimum steric separation” may generally refer to twice aminimum steric radius r_(R) of an R group in a bulky chemicalperforation reagent R-Het* employed to make the discrete pores. Methodsof chemical perforation using bulky reagents R-Het* and details of Rgroups and minimum steric radii r_(R) are generally described furtherwith respect to FIGS. 3A-5E.

In various examples, the pores may be characterized by one or morecarbon vacancy defects in the graphene monolayer such that the graphenelayer has substantially uniform pore sizes throughout. In some examples,each of the pores may be characterized by one or more carbon vacancydefects in the graphene monolayer such that the pores have substantiallythe same number of carbon vacancy defects throughout.

As used herein, a “carbon vacancy defect” may be a pore in a graphenemonolayer which may be defined by the absence of one or more carbonatoms compared to a graphene monolayer without a carbon vacancy defect.

As used herein, a “substantially uniform pore size” means that thediscrete pores may be characterized by substantially the same number ofone or more carbon vacancy defects per discrete pore. For example, inFIG. 1C, discrete pores 108 may be characterized as single-carbonvacancy defects corresponding to the absence of carbon atoms 102 fromgraphene monolayer 100 in FIG. 1B. In another example, in FIG. 1E,discrete pores 122 may be characterized as double-carbon vacancy defectscorresponding to the absence of carbon atoms 114 and 116 from graphenemonolayer 100 in FIG. 1D. In various examples, discrete pores ofsubstantially uniform pore size may have their carbon vacancy defectsarranged in substantially the same relative lattice positions withineach discrete pore. For example, a plurality of substantially uniformpores that include six carbon vacancy defects each may correspond toremoval of a six membered ring of carbon atoms in the hexagonal graphenelattice. In another example, a plurality of substantially uniform poresthat include six carbon vacancy defects each may correspond to removalof a six membered staggered linear chain of carbon atoms in thehexagonal graphene lattice.

As used herein, “substantially uniform pore sizes throughout” means thatat least about 80% of the discrete pores in a perforated graphenemonolayer may have a substantially uniform pore size. In variousexamples, the percentage of discrete pores in a perforated graphenemonolayer that may have a substantially uniform pore size may be: about85%, about 90%, about 95%, about 96%, about 97%, about 98%, about 99%,about 99.5%, or about 99.9%. In some examples, all of the discrete poresin a perforated graphene monolayer may have a substantially uniform poresize.

As used herein, “substantially the same number of one or more carbonvacancy defects” in relation to the plurality of discrete pores meansthat such discrete pores differ from each other by at most about threecarbon vacancy defects. For example, a plurality of pores havingsubstantially the same number of one or more carbon vacancy defects mayrange between one and three carbon vacancy defects per pore. In variousexamples, discrete pores may vary in number of carbon vacancy defects byabout three, about two, or about one. In some examples, each of theplurality of discrete pores has the same number of carbon vacancydefects. For example, in FIG. 1C, discrete pores 108 may becharacterized as having a single carbon vacancy defect per pore. Inanother example, in FIG. 1E, discrete pores 122 may be characterized ashaving a two-carbon vacancy defect per pore. In other examples, at leastabout 80% of the discrete pores in a perforated graphene monolayer maythe same number of carbon vacancy defects. In various examples, thepercentage of discrete pores in a perforated graphene monolayer that mayhave the same number of carbon vacancy defects may be: about 85%, about90%, about 95%, about 96%, about 97%, about 98%, about 99%, about 99.5%,or about 99.9%. In some examples, all of the discrete pores in aperforated graphene monolayer may have the same number of carbon vacancydefects.

As used herein, the “number” of carbon vacancy defects in reference to“substantially the same number of one or more carbon vacancy defects”means about one or more carbon defects, or in some examples at leastabout two carbon defects.

FIG. 2A is a conceptual drawing of a side view of an example membrane200 that includes a perforated graphene monolayer 106 configured incontact with a permeable substrate 202. Perforated graphene monolayer106 may include discrete pores 108. A substrate such as permeablesubstrate 202 may be configured to contact one or both sides of anexample perforated graphene monolayer such as 106.

As used herein, a “permeable substrate”, for example permeable substrate302, may be any material that may be employed to provide support to aperforated graphene monolayer such as 106. As used herein, a “permeablesubstrate” may also be permeable to at least one atomic or molecularspecies that traverses the discrete pores in the perforated graphenemonolayer. Suitable permeable substrates may include“solution-diffusion” solid membranes that permit atomic or molecularspecies to diffuse through the solid material of the permeablesubstrate. Suitable permeable substrates may also be configured asporous membranes, non-woven materials, or filters having pores, voids,channels, or the like, through which atomic or molecular species maytravel. Suitable materials for the permeable substrate may include, forexample, one or more of polyethylene including ultra high molecularweight polyethylene, polypropylene, polyester, polyurethane,polystyrene, polyolefin, aramide, aromatic polyester, carbon fiber,polysulfone and/or polyethersulfone. Suitable permeable substrates mayalso include metal meshes and porous ceramics. In various examples,suitable polymeric materials for the permeable substrate may becharacterized by a minimum molecular weight cutoff at: about 1,000,000daltons; about 500,000 daltons; about 250,000 daltons; or about 100,000daltons. In some examples, a suitable permeable substrate may include apolyether sulfone membrane characterized by a maximum molecular weightcutoff of about 100,000 daltons.

FIG. 2B is a conceptual drawing of a side view of an example membrane200 that may include a perforated graphene monolayer 106 arranged incontact with a permeable substrate 202. Perforated graphene monolayer106 may include discrete pores 108. In FIG. 2B, membrane 200 separates achamber 204 and a chamber 206. Chamber 204 may be configured to containa fluid mixture of two compounds 208 and 210. Chamber 206 may beconfigured for receiving a purified selection of one of compounds 208and 210. FIG. 2B depicts the fluid mixture, including first compound208, symbolized by dark-filled circles, and second compound 210,symbolized by white-filled circles. The first and second compounds mayalso include one or more differences in atomic or chemical charactersuch as differences in elemental composition, isotopic composition,molecular structure, size, mass, hydrophobicity, polarity,polarizability, charge distribution, or the like. For example, the firstcompound 208 may be smaller than the second compound 210 as symbolizedby the relative sizes of the filled circles in FIG. 2B. In someexamples, discrete pores such as 108 may be characterized by a diameterthat may be selective for passage of the first compound compared to thesecond compound. The diameter may select for passage of first compound208 compared to second molecule 210 based on the one or more differencesin atomic or chemical character, e.g., size, ionic nature, chemicalaffinity for the example membrane, or the like.

The fluid mixture of compounds 208 and 210 may be contacted to membrane200. First compound 208 may be directed from chamber 204 through pores108 to chamber 206 to separate first compound 208 from second compound210. The first compound 208 may be directed through discrete pores 108by employing a gradient across the graphene monolayer. The gradient mayinclude differences in one or more properties such as temperature,pressure, concentration, electric field, or electrochemical potential.

As used herein, a “fluid mixture” may be any fluid phase, e.g., gasphase, liquid phase, or supercritical phase, which may include at leasta first molecular species and a second molecular species, e.g.,compounds 208 and 210. In various examples, the fluid mixture mayinclude: a mixture of gases; a mixture of a vapor in a gas; a mixture ofliquids; a solution of a gas dissolved in a liquid; a solution of asolid dissolved in a liquid; a solution of a gas, liquid or solid in asupercritical fluid; or the like. In some examples, the fluid mixturemay be in contact with other phases of the two or more differentcompounds. For example, a fluid mixture that includes fluid phase carbondioxide as one of the compounds may be in contact with solid phasecarbon dioxide.

The first and second compounds may include compounds consisting of asingle atom, for example, helium, neon, argon, krypton, xenon, andradon. The compounds may also include compounds of two or more atomsconnected by one or more covalent bonds, ionic bonds, coordinationbonds, or the like. For example, suitable molecules may include water,hydrogen, nitrogen, oxygen, carbon monoxide, carbon dioxide, sulfurdioxide, hydrogen sulfide, a nitrogen oxide, a C1-C4 alkane, a silane,an organic solvent, or a haloacid. An “organic solvent”, as used herein,is a carbon based compound that typically is in liquid form when at anapproximate temperature of 25° C. with an approximate atmosphericpressure of 1 atm. Organic solvents may include, for example,acetonitrile; alcohols such as methanol, ethanol, propanol, 2-propanol,1-butanol, tertiary butanol, ethylene glycol, propylene glycol, or thelike; alkanes such as pentane, hexane, heptanes, cyclopentane,cyclohexane, cycloheptane, or the like; ethers such as dimethyl ether,diethyl ether, tetrahydrofuran, glyme, diglyme, or the like; halogenatedsolvents such as dichloromethane, chloroform, carbon tetrachloride,trichloroethylene, or the like; aromatics such as benzene, toluene,xylenes, or the like; or polar aprotic solvents such as dimethylsulfoxides, dimethyl formamide, or the like.

In some examples, the second molecule may be a liquid, e.g., water or anorganic solvent, and the first molecule may be a covalent or ionicmolecular compound dissolved in the liquid.

In some examples, one molecule may be a polar liquid such as water, andthe other molecule may be a salt that includes a cation and an anion.Examples of cations for salts may include metal cations, e.g. alkalimetal cations such as lithium, sodium, potassium, or the like; alkaliearth metal cations such as calcium or magnesium, or the like; cationsof transition metals such as copper, iron, nickel, zinc, manganese, orthe like; cations of metals in other groups, such as cations ofaluminum; and so on. Examples of anions for salts may include, but arenot limited to, fluoride, chloride, bromide, iodide, chlorate, bromate,iodate, perchlorate, perbromate, periodate, hydroxide, carbonate,bicarbonate, sulfate, phosphate, and so on. In some examples, the fluidmixture may be a natural water source such as seawater or groundwater,where the perforated graphene membrane may be employed to separate waterfrom natural solutes, such as sodium chloride, and/or unnatural solutes,such as molecules that are manmade pollutants.

As used herein, “separation selectivity” means a ratio of perforatedgraphene monolayer permeability rates between specific pairs of atomicor molecular species, for example, molecules 208 and 210 in FIG. 2B. Forexample, theoretical calculations have been described for a one-atomthick monolayer characterized by pores about 2.5 angstroms in diameter;the ratio of a calculated hydrogen permeability rate divided by acalculated methane permeability rate was 10^²³:1. In comparison,currently known “solution diffusion” polymer membranes have a hydrogento methane separation selectivity of about 150:1. Perforated graphenemonolayers described herein may be characterized by a separationselectivity, for example, perforated graphene monolayers 106 in FIG. 1C,120 in FIG. 1E, and 106 in membrane 200 in FIG. 2A and FIG. 2B. Forexample, an example perforated graphene monolayer such as 106 mayinclude about one carbon vacancy defect per pore. A hydrogen:methaneseparation selectivity for perforated graphene monolayer 106 may becharacterized as the ratio of permeation rates of molecular hydrogen(H₂) compared to methane (CH₄). In some examples, the hydrogen:methaneseparation selectivity may be at least about 200:1; or in variousexamples, between about 200:1 and about 10²³:1, for example, at leastabout: 10³:1; 10⁴:1; 10⁵:1; 10⁶:1; 10⁹:1; 10¹²:1; 10¹⁵:1; 10¹⁸:1; or10²¹:1.

FIG. 3A is a conceptual drawing showing a method of forming a pluralityof discrete pores 108 in a graphene monolayer 100 to form perforatedgraphene monolayer 106. FIG. 3A shows a side view of graphene monolayer100. A reagent R-Het* may be contacted to a plurality of locations at agraphene monolayer such as graphene monolayer 100. The reagent may becontacted to the graphene monolayer in any suitable form, such as asolid, a liquid, a gas, a solute in a solution, particles in asuspension, or the like. The reagent may be contacted to the graphenemonolayer by any suitable means, such as by: immersion; spin coating;dip coating; selective coating, e.g., applied via an ink-jet typenozzle; sublimation or condensation; chemical vapor deposition; or thelike.

FIG. 3A also shows that at graphene monolayer 100, the reagentrepresented by R-Het* may be reacted with at least one graphene carbonatom C_(g) at each of the plurality of locations, e.g., C_(g) 304 and306. The reaction forms heteroatom-carbon moieties represented byR-Het-C_(g) 300 and 302 in modified graphene monolayer 100′. Modifiedgraphene monolayer 100′ may be represented by the formula[R-Het-C_(g)]_(p)graphene, where p represents the number of locations inthe plurality of locations.

FIG. 3A also shows that at graphene monolayer 100′, steric interactionsbetween adjacently located R-Het-C_(g) 300 and 302 provide a minimumseparation distance 104. The side view shown in FIG. 3A may be comparedto the top view shown in FIGS. 1B and 1C. The R groups, symbolized bythe shaded spheres in FIG. 3A, may be selected to provide a minimumsteric radius r_(R). The phrase “minimum steric radius r_(R)” means therelative orientation of respective R groups that provides minimumseparation distance 104 of at least about 2*r_(R). The shaded spheresrepresenting the R groups in FIG. 3A correspond to circles 105 and 119shown in FIGS. 1B, 1C, 1D and 1E. The minimum steric distance 104provided by using the R groups may substantially reduce the chance ofR-Het-C_(g) derivitizing adjacent carbon-carbon bonds in graphene. Invarious examples, the steric interactions may isolate Het-C_(g) bondsfrom each other. In various examples, the steric interactions may leadto discrete pore formation, whereby graphene carbon radicals created byremoving Het-C_(g) may be unlikely to combine or rearrange into largerpores.

The group represented by R may be one of —R^(a), —SO₂R^(a), —(CO)OR^(a),or —SiR^(a)R^(b)R^(c); where R^(a), R^(b), and R^(c) are eachindependently alkyl, aryl, heteroaryl, aralkyl, or heteroaralkyl. Invarious examples, the alkyl, aryl, heteroaryl, aralkyl, andheteroaralkyl groups represented by R^(a), R^(b), and R^(c) may besubstituted or unsubstituted. In some examples, the groups representedby R^(a), R^(b), and R^(c) may be unsubstituted.

The group Het* may be any heteroatom group which reacts with carbonsC_(g) or carbon-carbon double bonds C_(g)═C_(g) in graphene to formheteroatom-carbon moieties, e.g., as represented by R-Het-C_(g) 300 and302. Examples of heteroatom groups represented by Het* may includenitrene radical, or an activated oxy group such as oxy radical, oxyanion, hydroxyl, carboxyl, or carboxylate; or the like. Activatedheteroatom reagents represented by R-Het* may be prepared by activatingprecursor compounds represented by R-Het. Various examples of reactingheteroatom groups with graphene are discussed in the descriptions ofFIGS. 5A, 5B, 5C, 5D, and 5E.

FIG. 3A also shows that perforated graphene monolayer 106, includingdiscrete pores 108, may be formed by removing heteroatom-carbon moietiesrepresented by R-Het-C_(g) 300 and 302 at modified graphene monolayer100′. Discrete pores 108 are characterized by carbon vacancy defects inthe graphene monolayer defined by removing the graphene carbon atomsC_(g) from the plurality of locations such that the graphene monolayerhas substantially uniform pore sizes throughout.

FIG. 3B is a conceptual drawing showing additional operations which maybe included in a method of forming a plurality of discrete pores 108 ina graphene monolayer 100 to form perforated graphene monolayer 106. Forexample, FIG. 3B shows an operation of activating a precursor R-Het toform the activated reagent R-Het*. In another example of an additionaloperation, FIG. 3B shows that the heteroatom-carbon moieties representedby R-Het-C_(g) 300 and 302 may be removed by employing additionaloperations. For example, as shown in FIG. 3A, the R groups may beremoved to provide groups H-Het*-C_(g) 301 and 303, followed by removalof H-Her-Cg 301 and 303 and passivation with hydrogen to providediscrete pores 108 in perforated graphene monolayer 106.

FIG. 4 depicts an example reaction scheme corresponding to the generalscheme shown in FIG. 3A and FIG. 3B. In FIG. 4, trimethyl silyl azide400, corresponding to R-Het in FIGS. 3A and 3B, may be first heated orphotolyzed to produce the activated trimethyl silyl nitrene radical 402.For example, graphene 404 may be placed in an evacuated reactionchamber. Trimethyl silyl azide 400 may be degassed and evaporated to apressure between about 0.1 Torr and about 10 Torr, for example about 1Torr. The chamber may be heated, for example, between about 150° C. andabout 250° C., for example, about 200° C. Trimethyl silyl nitreneradical 402 may be reacted with a carbon carbon double bond in graphene404 to form the trimethyl silyl aziridine compound 406, corresponding toR-Het-C_(g) in FIGS. 3A and 3B. Referring to FIG. 3A, the Het group inR-Het-C_(g) 300 and 302 bonds to at least one carbon C_(g). In theexample shown in FIG. 4, the nitrene radical bonds to two carbons toform the three-membered aziridine ring in compound 406. The specificexample in FIG. 4 also shows that the trimethyl silyl group in compound406, corresponding to R, may be cleaved, e.g., with a fluoride ionsource such as tetrabutyl ammonium fluoride to form the N—H aziridinering in compound 408.

FIG. 5A depicts an example reaction scheme corresponding to a portion ofthe general scheme shown in FIG. 3A and FIG. 3B. Graphene monolayer 500may be contacted with a plurality of substituted nitrene radicals 501. Aplurality of carbon-carbon double bonds C_(g)═C_(g) in graphenemonolayer 500 may react with the substituted nitrene radicals 501. Agraphene monolayer may be formed that may be functionalized with aplurality of N—R substituted aziridine groups as represented byaziridine structure 502. The N—R substituents of the aziridine groupsmay be cleaved to form an N—H aziridine structure 504.

In various examples, a suitable nitrene precursor group represented by-Het may be azide, —N₃. In some examples, R-Het* may be prepared asR-nitrene 501 by reacting an azide precursor represented by R—N₃ underthermolytic or photolytic conditions suitable for converting azide tonitrene. In some examples, suitable values for R when -Het is azide mayinclude —R^(a) or —SiR^(a)R^(b)R^(c). In various examples, reaction ofR-nitrene with graphene produces an N—R aziridine 502 as shown in FIG.5A.

In some examples, R in aziridine structure 502 may be—SiR^(a)R^(b)R^(c). In various examples, groups such as—SiR^(a)R^(b)R^(c) may be cleaved from the substituted aziridinerepresented by structure 502 by contacting each substituted aziridine502 with one of: a quaternary ammonium fluoride; an alkyl sulfonic acid;an aryl sulfonic acid; trifluoromethane sulfonic acid; an alkali metalhydroxide; or an oxidant.

In various examples, when R may be —(CO)OR^(a), a suitable nitreneprecursor group represented by -Het may be —N—OSO₂—R^(f), wherein R^(f)may be a methanesulfonate, trifluoromethanesulfonate,bromophenylsulfonate, methylphenylsulfonate or nitrophenylsulfonategroup. In some examples, R-Het* may be prepared as R-nitrene 501 byreacting a nitrene precursor represented by R^(a)O(CO)—N—OSO₂—R^(f) withan amine base such as triethylamine. In various examples, reaction ofR-nitrene with graphene produces an N—R aziridine 502 as shown in FIG.5A.

In various examples, when R may be —(SO₂)R^(a′), a suitable nitreneprecursor group represented by -Het may be —NH₂. In some examples,R^(a′) may be substituted or unsubstituted alkyl, aryl, heteroaryl,aralkyl, or heteroaralkyl. In various examples, R^(a′) may be an alkyl,fluoroalkyl, bromophenyl, alkylphenyl or nitrophenyl group, which may befurther substituted. In some examples, R-Het* may be prepared asR-nitrene 501 by reacting a nitrene precursor represented byR^(a)—SO₂—NH₂ with PhI(O(CO)CH₃)₂ in the presence of a copper,palladium, or gold catalyst. Example catalysts may include copperacetylacetonate, palladium tetrakis acetylacetonate, gold4,4′,4″-tri-tert-butyl-2,2′:6′,2″-terpyridine triflate, or the like. Thereaction may be conducted in situ with a graphene monolayer. In someexamples, R^(a)—SO₂—NH₂ may be reacted with PhI(O(CO)CH₃)₂ with analkaline metal hydroxide, e.g., KOH, in an alcohol, e.g. methanol, toform R^(a)—SO₂—N═IPh. The isolated R^(a)—SO₂—N═IPh may be then bereacted with a copper, palladium, or gold catalyst such as copperacetylacetonate to produce R-Het* as R-nitrene. In various examples,reaction of R-nitrene with graphene produces an N—R aziridine 502 asshown in FIG. 5A.

In some examples, R in aziridine structure 502 may be —(CO)OR^(a). Invarious examples, groups such as —(CO)OR^(a) may be cleaved from thesubstituted aziridine represented by structure 502 by contacting eachsubstituted aziridine 502 with one of: an alkali alkylthiolate; atrialkyl silyl iodide; an alkali metal hydroxide; an alkali earth metalhydroxide; potassium carbonate; HBr/acetic acid; sodiumbis(2-methoxyethoxy)aluminum hydride; sodium tellurium hydride; apotassium trialkylsiloxide; an alkyl lithium; a quaternary ammoniumfluoride; an acyl chloride with sodium iodide; an alkyl sulfonic acid;trifluoromethane sulfonic acid; or an aryl sulfonic acid.

In some examples, R in aziridine structure 502 may be —SO₂R^(a). Invarious examples, groups such as —SO₂R^(a) may be cleaved from thesubstituted aziridine represented by structure 502 by contacting eachsubstituted aziridine 502 with one of: HBr and acetic acid; HBr andphenol; HF and pyridine; sodium bis(2-methoxyethoxy)aluminum hydride; analkali metal arylide salt; an alkali metal in ammonia oriso-propylamine; sodium-potassium alloy adsorbed on silica gel; samariumiodide; perchloric acid in acetic acid; photolysis in the presence ofether; photolysis in the presence of sodium borohydride anddimethoxybenzene; photolysis in the presence of hydrazine; photolysis inthe presence of borane:ammonia; photolysis in the presence of sodiumborohydride and beta-naphthoxide; or sodium amalgam in the presence ofsodium monohydrogen phosphate.

In some examples, R in aziridine structure 502 may be —R^(a). In variousexamples, groups such as —R^(a) may be cleaved from the substitutedaziridine represented by structure 502 by contacting each substitutedaziridine 502 with one of: hydrogen in the presence of catalyticpalladium; borane in the presence of catalytic palladium; borane in thepresence of catalytic Raney nickel; or hydrogen peroxide followed bytetrasodium 5,10,15,20-tetra(4-sulfophenyl) porphyrinatoiron(II).

FIG. 5B depicts an example reaction scheme corresponding to a portion ofthe general scheme shown in FIG. 3A and FIG. 3B which may be employedfor forming pores containing single carbon vacancy defects. In variousexamples, N—H aziridine moieties represented by structural formula 504may be heated. In some examples, N—H aziridine moieties represented bystructural formula 504 may be heated in the presence of hydrogen gas.Suitable temperatures range from between about 700° C. to about 900° C.,in various examples between about 750° C. to about 850° C., or in someexamples about 800° C. Suitable reaction times range from about 1 minuteto about 12 hours, in various examples from about 10 minutes to about 4hours, in some examples from about 15 minutes to about 2 hours, or inother examples, about 30 minutes. In various examples, suitable hydrogengas conditions range from a pressure of hydrogen from about 1 Torr toabout 7600 Torr; in some examples from about 1 Torr to about 760 Torr;or in other examples, from about 10 Torr to about 100 Torr, for example,50 Torr. Other suitable hydrogen gas conditions may include a flow ofhydrogen gas from about 1 sccm to about 25 sccm, in various examplesfrom about 1 sccm to about 5 sccm, or in some examples about 3 sccm. TheN—H group and one Cg may be thermolytically cleaved from the surface ofstructure 504. Passivation with hydrogen may provide structure 506, agraphene monolayer with a pore defined by the removal of a singlegraphene carbon Cg. Perforated graphene structure 506 corresponds to thesingle-carbon vacancy defect of discrete pore 108, for example asdepicted in perforated graphene monolayer 106 in FIG. 1C.

FIG. 5C depicts an example reaction scheme corresponding to a portion ofthe general scheme shown in FIG. 3A and FIG. 3B which may be employedfor forming pores containing double carbon vacancy defects. In variousexamples, the N—H aziridine moieties represented by structure 504 may behydrolyzed to produce beta-amino alcohol moieties each represented bystructural formula 508. The hydrolysis reaction may be conducted bycontacting structure 504 with a basic aqueous solution of an alkalimetal hydroxide or an alkaline earth metal oxide or hydroxide. Thehydrolysis reaction may employ the basic aqueous solution in aconcentration range from about 0.1 molar to about 10 molar, for example,about 1 molar. In various examples, the hydrolysis reaction may beconducted at a temperature between: about 0° C. and about 100° C.; about10° C. and about 90° C.; about 20° C. and about 80° C.; or about 25° C.and about 75° C.; The hydrolysis reaction may be followed by rinsingwith water and/or an aqueous buffer solution, for example, a pH 7 buffersolution.

Following the hydrolysis reaction, the plurality of N—H aziridinemoieties represented by structural formula 508 may be heated underhydrogen to a temperature between about 750° C. and about 900° C. toproduce the plurality of pores in the graphene monolayer as a pluralityof double-carbon vacancy defects each represented by structural formula510. The Cg-NH₂ and Cg-OH groups may be may be thermolytically cleavedfrom the surface of beta-amino alcohol structure 508. Thermolyticcleavage may evolve one or more gases, for example, hydrogen cyanide,hydrogen, carbon monoxide, ammonia, water, or the like. Passivation withhydrogen may be employed to provide structure 510, a graphene monolayerwith a pore defined by the removal of two graphene carbons Cg.Perforated graphene structure 510 corresponds to the double-carbonvacancy defect of discrete pore 122, for example as depicted inperforated graphene monolayer 120 in FIG. 1E.

FIG. 5D depicts an example reaction scheme corresponding to a portion ofthe general scheme shown in FIG. 3A and FIG. 3B, which employs a 1,2diether to form a 1,2 diol intermediate compound represented bystructure 514. Graphene monolayer 500 may be contacted with an activatedoxy reagent represented by R-Het*, wherein R may be —R^(a). Theactivated oxy reagent represented by R-Het* may be prepared by combininga suitable precursor of an activated oxy reagent represented by R-Hetwith an activating reagent, such as a trivalent iodosoaryl reagent.Suitable iodosoaryl reagents may include, for example, iodosobenzenetetrafluoroborate, iodosobenzene hexafluoroantimonate, iodosobenzenehexafluorophosphate, or the like.

Trivalent iodosoaryl reagents may be prepared by combining a chloroformsolution of (diacetoxyiodo)benzene with an aqueous solution of asuitable acid, e.g., tetrafluoroboric acid, hexafluoroantimonic acid, orhexafluorophosphoric acid. The mixture may be evaporated under vacuum at40° C. to 50° C. The product, e.g., iodosobenzene tetrafluoroborate,iodosobenzene hexafluoroantimonate, or iodosobenzenehexafluorophosphate, may be crystallized by adding a small amount ofwater.

Suitable precursors of activated oxy reagents represented by R-Het,wherein R may be —R^(a) may include alcohols of formula R—OH, salts ofR—O⁻ with alkaline metal cations, salts of R—O⁻ with alkaline earthmetal cations, or the like. Carbon-carbon double bond C_(g)═C_(g) ingraphene monolayer 500 may react in the presence of the trivalentiodosoaryl reagent and R-Het* to form a graphene monolayerfunctionalized with a 1,2-diether represented by structure 512.

In various examples, the RO ether groups may be cleaved from structure512 to form the 1,2 diol intermediate compound represented by structure514. In various examples, 1,2 diether structure 512 may be reacted withone or more of hydrobromic acid, hydroiodic acid, boron tribromide, oraluminium trichloride.

FIG. 5E depicts an example reaction scheme corresponding to a portion ofthe general scheme shown in FIG. 3A and FIG. 3B, which employs a 1,2diester moiety to form the 1,2 diol intermediate compound represented bystructure 514.

Referring to FIG. 5E, in various examples, graphene monolayer 500 may bereacted with a trivalent iodosoaryl reagent and a carboxyl precursorR-Het, wherein R may be —R^(a).

In various examples, the trivalent iodosoaryl reagent may include, forexample, iodosobenzene tetrafluoroborate, iodosobenzenehexafluoroantimonate, or iodosobenzene hexafluorophosphate, prepared asdescribed under the description for FIG. 5D.

In various examples, suitable carboxyl precursors of activated oxyreagents represented by R-Het, wherein R may be —R^(a) may include:carboxylic acids of formula R—CO₂H; salts of R—CO₂ ⁻ with alkaline metalcations; salts of R—CO₂ with alkaline earth metal cations; or the like.Carbon-carbon double bond C_(g)═C_(g) in graphene monolayer 500 mayreact with the trivalent iodosoaryl reagent and the carboxyl precursorrepresented by R-Het to form a graphene monolayer functionalized with a11,2-diester moiety represented by structure 518.

Referring to FIG. 5E, in various examples, the iodosylaryl reagent andthe carboxyl precursor R-Het may together form a complex correspondingto R-Het*. For example, R-Het* may represent(bis(R—CO₂)iodo(III))benzene, which may be formed by reacting benzene,potassium peroxodisulfate, elemental iodine, and R-Het ═R—CO₂H in thepresence of concentrated sulfuric acid. In various examples, graphenemonolayer 500 may be reacted with bis(R—CO₂)iodo(III))benzene and acopper(I) or copper(II) salt of: trifluoromethanesulfonate; perchlorate;methanesulfonate; sulfonate; methylphenylsulfonate;bromophenylsulfonate; nitrophenylsulfonate; or the like. Carbon-carbondouble bond C_(g)═C_(g) in graphene monolayer 500 may react with thebis(R—CO₂)iodo(III))benzene to form a graphene monolayer functionalizedwith a 1,2-diester moiety represented by structure 518.

Referring to FIG. 5E, in various examples, the RCO₂-Cg carboxyl groupsin 1,2-diester moiety 518 may be hydrolyzed to form the 1,2 diolcompound represented by structure 514. In various examples, suitableconditions may include contacting 1,2-diester moiety 518 with an acid orbase under conditions suitable for hydrolyzing the 1,2-diester moiety518 to form the 1,2 diol compound represented by structure 514. Invarious examples, suitable acids may include HF, HCl, HBr, HI, H₂SO₄,phosphoric acid, methanesulfonic acid, trifluoromethanesulfonic acid,methylphenylsulfonic acid; bromophenylsulfonic acid; nitrophenylsulfonicacid, or the like. In various examples, suitable conditions may includecontacting 1,2-diester moiety 518 with a base, for example, an alkalinemetal hydroxide, an alkaline earth metal hydroxide, an alkaline earthmetal oxide, or the like. In some other examples, a suitable base mayinclude a quaternary ammonium hydroxide, for example,tetramethylammonium hydroxide, tetrabutylammonium hydroxide, or thelike. In various examples, a quaternary ammonium salt may be added, forexample, tetrabutylammonium sulfate, tetraethylammonium bromide, or thelike. In various examples, suitable conditions may include providing asource of water. In various examples, suitable conditions may include abiphasic system including an aqueous phase and an organic phase, wherethe organic phase may include tetrahydrofuran, dioxane, diethyl ether,or the like. In various examples, suitable conditions may includeheating between about 20° C. and about 100° C. In various examples,wherein a biphasic system may be employed, suitable conditions mayinclude heating between about 20° C. and about the boiling temperatureof the organic phase, e.g., tetrahydrofuran.

Referring again to FIG. 5D and FIG. 5E, in various examples, the 1,2diol intermediate compound represented by structure 514 may bethermolytically cleaved and passivated to provide structure 516, agraphene monolayer with a pore defined by the removal of two graphenecarbons Cg. The 1,2 diol intermediate compound represented by structure514 may be heated. In some examples, 1,2 diol intermediate compoundrepresented by structure 514 may be heated in the presence of hydrogengas. Suitable temperatures range from between about 700° C. to about900° C., in various examples between about 750° C. to about 850° C., orin some examples about 800° C. Suitable reaction times range from about1 minute to about 12 hours, in various examples from about 10 minutes toabout 4 hours, in some examples from about 15 minutes to about 2 hours,or in other examples, about 30 minutes. In various examples, suitablehydrogen gas conditions range from a pressure of hydrogen from about 1Torr to about 7600 Torr; in some examples from about 1 Torr to about 760Torr; or in other examples, from about 10 Torr to about 100 Torr, forexample, 50 Torr. Other suitable hydrogen gas conditions may include aflow of hydrogen gas from about 1 sccm to about 25 sccm, in variousexamples from about 1 sccm to about 5 sccm, or in some examples about 3sccm. The two Cg-OH groups may be thermolytically cleaved from thesurface of structure 514. Thermolytic cleavage may evolve one or morespecies, for example, hydrogen, hydroxyl, carbon monoxide, carbondioxide, water, or the like. Passivation with hydrogen may be employedto provide structure 516, a graphene monolayer with a pore defined bythe removal of two graphene carbons Cg. Perforated graphene structure516 corresponds to the double-carbon vacancy defect of discrete pore122, for example as depicted in perforated graphene monolayer 120 inFIG. 1D.

Example embodiments may also include methods of making an exampleperforated graphene monolayer or an example membrane that may include anexample perforated graphene monolayer as described herein. These methodsmay be implemented in any number of ways, including the structuresdescribed herein. One such way may be by machine operations, of devicesof the type described in the present disclosure. Another optional waymay be for one or more of the individual operations of the methods to beperformed in conjunction with one or more human operators performingsome of the operations while other operations may be performed bymachines. These human operators need not be collocated with each other,but each can be only with a machine that performs a portion of theprogram. In some other examples, the human interaction may be automatedsuch as by pre-selected criteria that may be machine automated.

FIG. 6 is a flow diagram showing operations that may be used in makingan example perforated graphene monolayer, such as perforated graphenemonolayers 106 or 120, or corresponding membranes such as membrane 200in accordance with at least some embodiments described herein.

A method of making an example perforated graphene monolayer such as 106or 120 may include one or more operations, actions or functions asillustrated by one or more of blocks 622, 624, 626, 628, and/or 630. Themethod may begin with an operation 622, “CONTACT R-HET* TO PLURALITY OFLOCATIONS AT GRAPHENE MONOLAYER”, such as graphene monolayer 100. Thereagent may be contacted to the graphene monolayer in any suitable form,such as a solid, a liquid, a gas, a solute in a solution, particles in asuspension, or the like. The R-Het* reagent may be contacted to thegraphene monolayer by any suitable apparatus or method, such as byemploying: a solution coating apparatus; a spin coating apparatus; a dipcoating apparatus; selective coating apparatus, e.g., applied via apressurized fluid applicator, e.g., an ink-jet type nozzle; sublimationor condensation using a condenser, a vacuum chamber, and/or a heater;chemical vapor deposition; or the like. Controller device 610 mayoperate “MIXER/REACTOR/R-HET* ADDITION/APPLICATOR” machine 792 toperform operation 622. Machine 792 may include one or more mixingfunctions, such as mechanical stirring, heating, ultrasonication fordissolving and/or reacting reagents as described above. Machine 792 mayalso include one or more application or coating functions for contactingreagents such as R-Het* to the graphene. At operation 622, manufacturingcontroller 790 may instruct machine 792 with parameters regarding, forexample, the extent of mechanical stirring or reaction based on thereagents employed. Operation 622 may be continued until a desired pointmay be reached, e.g., the reaction has proceeded for a sufficient lengthof time to functionalize the surface of the graphene monolayer.

In some examples, the R-Het* reagent may be prepared in the presence ofthe graphene monolayer by activating a R-Het* precursor to form anactivated heteroatom such as R-nitrene, [RO] or [RCO₂], as discussedabove under FIGS. 5A, 5B, 5C, 5D, and 5E. In various examples, suitablereagent activator apparatus may include one or more of: a resistiveheating element; an infrared laser; an ultraviolet light source; and/orone or more reagent reservoirs, e.g., a reaction chamber configured tocontact a precursor compound R-Het and a trivalent iodosoaryl compound;or the like.

Referring again to FIG. 6, the method may include an operation 624,“PROVIDE SEPARATION DISTANCE BETWEEN LOCATIONS”, such as separationdistances 104 or 118. In various examples, the separation distance maybe provided by selecting an R group with the desired amount of stericbulk, where the separation distance may be at least about twice theminimum steric radius r_(R) of group R. In some examples, the separationdistance may be increased, for example, by running the reaction at a lowconcentration of R-Het* such that the surface of the graphene monolayermay be sparsely reacted. In some examples, the separation distance maybe modulated indirectly by contacting graphene monolayer with R-Het* atselected locations via patterned application of R-Het* using apressurized fluid applicator, or the like.

The method may include an operation 626, “REACT EACH R-HET* WITHGRAPHENE CARBON AT EACH LOCATION”. In some examples, the reaction mayoccur upon contact of R-Het* with the graphene monolayer. In otherexamples, a R-Het may be activated at selected sites at the graphenemonolayer. For example, when R-Het may be R-azide, an ultraviolet lightsource such as an ultraviolet lamp, an ultraviolet light emitting diode,or a collimated light source such as an ultraviolet laser may be used tophotolytically generate R-Het* as R-nitrene. In some examples, acollimated light source such as an ultraviolet laser may be used tophotolytically generate R-Het* as R-nitrene at specific sites on thegraphene monolayer. Controller device 610 may operate“HEATER/PHOTOLYZER” machine 794, optionally in conjunction with machine792 to perform operations 624 and 626. Controller device 610 may providemachine 792 and/or machine 794 with parameters regarding, for example,the location and patterning of applying the R-Het* reagent, the locationand patterning of activating the R-Het* reagent from a R-Het precursor,e.g. by photolytic activation, heating, or the like. Operation 624 maybe continued until a desired point may be reached, e.g., the graphenemonolayer has had sufficient time to react to the desired level offunctionalization.

The method may include an operation 628, “FORM PORES BY CREATING CARBONVACANCY DEFECTS UNDER PASSIVATION CONDITIONS”, such as pores 108 and122. In some examples, pores such as 108 and 122 may be formed byheating a precursor such as aziridine 504, beta amino alcohol 508, 1,2diol 514, or the like. Suitable apparatus components for forming pores108 and 122 may include a heater, such as a resistive heating element oran infrared laser. Suitable apparatus components for forming pores 108and 122 may also include a hydrogen source, e.g., a reaction chamberconfigured to apply a partial pressure of hydrogen or a flow of hydrogenwhile heating may be conducted. Controller device 610 may also operate“HEATER/PHOTOLYZER” machine 794, optionally in conjunction with“HYDROGEN PASSIVATION SOURCE” 796 to perform operation 628. Operation628 may be continued until a desired point may be reached, e.g., thefunctionalized graphene monolayer has had sufficient time to react toform and passivate the discrete pores, such as pores 108 or 122.

The method may include an operation 630, “CONTACT GRAPHENE WITH PORES TOPERMEABLE SUPPORT SUBSTRATE”. Operation 630 may include preparing aperforated graphene monolayer as described herein from a graphenemonolayer produced on copper foil, e.g., 25 micrometer thick copperfoil. Operation 630 may also include one or more actions such as:depositing and curing a layer of a suitable transfer polymer on theperforated graphene monolayer; etching to remove the copper foil;washing the resulting perforated graphene monolayer/cured polymer;contacting the perforated graphene monolayer surface to a suitablepermeable substrate; redepositing and curing a second layer of polymer;washing the combined polymer layers away with a solvent such as acetone;and the like. Suitable polymers for operation 630 may include, forexample, polymethyl methacrylates. Suitable apparatus for operation 630may include apparatus for coating the polymethyl methacrylate, e.g.,solution coaters, spin coaters, dip coaters, and the like. Suitableapparatus for operation 630 may also include a curing oven orultraviolet light source for curing the polymethyl methacrylate.Additional suitable apparatus for operation 630 may include etching andwashing chambers. Further suitable apparatus for operation 630 mayinclude apparatus for contacting the perforated graphene monolayersurface to a suitable permeable substrate, such as a contact press. Atoperation 630, the processor (e.g., processor 610) may controlapplicator, mixer, and reactor functions of machine 792 to transfer theperforated graphene monolayer to a permeable substrate such as 302, toform a membrane such as 300. Operation 630 may include one or morefunctions such as: melt processing; solvent evaporation; reducedpressure solvent evaporation; spin coating; dip coating; spray coating;solvent casting; doctor blading; removal of solvent under supercriticalconditions; polymerization in situ from precursors of the polymer;curing or crosslinking the polymer in situ; contact printing; metaletching; polymer etching/dissolution; or the like.

In various examples, operations described herein may include contactingreagents to the graphene monolayer or perforated graphene monolayer. Forexample, operation 622 may include contacting a reagent R-Het* to agraphene monolayer; operation 630 may include contacting and curing apolymer to the perforated graphene monolayer; and the like. Such methodsmay include one or more techniques such as: melt processing; solventevaporation; reduced pressure solvent evaporation; spin coating; dipcoating; spray coating; ink-jet style printing; solvent casting; doctorblading; removal of solvent under supercritical conditions;polymerization in situ from precursors of the polymer; curing orcrosslinking the polymer in situ, or the like. Specific details ofsuitable polymer processing conditions may be selected based on theparticular R-Het* or polymer. For example, typical solution castingmethods employ high boiling solvents of the polymer in question.

The operations included in the process of FIG. 6 described above are forillustration purposes. A process of making an example perforatedgraphene monolayer or membrane as described herein may be implemented bysimilar processes with fewer or additional operations. In some examples,the operations may be performed in a different order. In some otherexamples, various operations may be eliminated. In still other examples,various operations may be divided into additional operations, orcombined together into fewer operations. Although illustrated assequentially ordered operations, in some implementations the variousoperations may be performed in a different order, or in some casesvarious operations may be performed at substantially the same time.

FIG. 7 is a block diagram of an automated machine 700 that may be usedfor making an example perforated graphene monolayer, in accordance withat least some embodiments described herein. As illustrated in FIG. 7,“MANUFACTURING CONTROLLER” 790 may be coupled to machines that may beused to carry out the operations described herein, for example,“MIXER/REACTOR/R-HET* ADDITION/APPLICATOR” 792, “HEATER/PHOTOLYZER” 794,“HYDROGEN PASSIVATION SOURCE” 796, and/or “SUPPORT SUBSTRATE APPLICATOR”798.

Manufacturing controller 790 may be operated by human control, or may bedirected by a remote controller 770 via network 710. Data associatedwith controlling the different processes of making the perforatedgraphene monolayers and membranes thereof may be stored at and/orreceived from data stores 780.

FIG. 8 illustrates a general purpose computing device that may be usedto control the automated machine 700 of FIG. 7 or similar manufacturingequipment in making an example perforated graphene monolayer or membranethereof, in accordance with at least some embodiments described herein.In a basic configuration 802, computing device 800 typically may includeone or more processors 804 and a system memory 806. A memory bus 808 maybe used for communicating between processor 804 and system memory 806.

Depending on the desired configuration, processor 804 may be of any typeincluding but not limited to a microprocessor (μP), a microcontroller(μC), a digital signal processor (DSP), or any combination thereof.Processor 804 may include one more levels of caching, such as a levelcache memory 812, a processor core 814, and registers 816. Exampleprocessor core 814 may include an arithmetic logic unit (ALU), afloating point unit (FPU), a digital signal processing core (DSP Core),or any combination thereof. An example memory controller 818 may also beused with processor 804, or in some implementations memory controller815 may be an internal part of processor 804.

Depending on the desired configuration, system memory 806 may be of anytype including but not limited to volatile memory (such as RAM),non-volatile memory (such as ROM, flash memory, etc.) or any combinationthereof. System memory 806 may include an operating system 820, one ormore manufacturing control applications 822, and program data 824.Manufacturing control application 822 may include a control module 826that may be arranged to control automated machine 700 of FIG. 7 and anyother processes, methods and functions as discussed above. Program data824 may include, among other data, material data 828 for controllingvarious aspects of the automated machine 700. This described basicconfiguration 802 is illustrated in FIG. 8 by those components withinthe inner dashed line.

Computing device 800 may have additional features or functionality, andadditional interfaces to facilitate communications between basicconfiguration 802 and any required devices and interfaces. For example,a bus/interface controller 830 may be used to facilitate communicationsbetween basic configuration 802 and one or more data storage devices 832via a storage interface bus 834. Data storage devices 832 may beremovable storage devices 836, non-removable storage devices 838, or acombination thereof. Examples of removable storage and non-removablestorage devices include magnetic disk devices such as flexible diskdrives and hard-disk drives (HDD), optical disk drives such as compactdisk (CD) drives or digital versatile disk (DVD) drives, solid statedrives (SSD), and tape drives to name a few. Example computer storagemedia may include volatile and nonvolatile, removable and non-removablemedia implemented in any method or technology for storage ofinformation, such as computer readable instructions, data structures,program modules, or other data.

System memory 806, removable storage devices 836 and non-removablestorage devices 838 may be examples of computer storage media. Computerstorage media may include, but is not limited to, RAM, ROM, EEPROM,flash memory or other memory technology, CD-ROM, digital versatile disks(DVD) or other optical storage, magnetic cassettes, magnetic tape,magnetic disk storage or other magnetic storage devices, or any othermedium which may be used to store the desired information and which maybe accessed by computing device 800. Any such computer storage media maybe part of computing device 800.

Computing device 800 may also include an interface bus 840 forfacilitating communication from various interface devices (e.g., outputdevices 842, peripheral interfaces 844, and communication devices 866 tobasic configuration 802 via bus/interface controller 830. Example outputdevices 842 may include a graphics processing unit 848 and an audioprocessing unit 850, which may be configured to communicate to variousexternal devices such as a display or speakers via one or more NV ports852. Example peripheral interfaces 544 may include a serial interfacecontroller 854 or a parallel interface controller 856, which may beconfigured to communicate with external devices such as input devices(e.g., keyboard, mouse, pen, voice input device, touch input device,etc.) or other peripheral devices (e.g., printer, scanner, etc.) via oneor more I/O ports 858. An example communication device 866 may include anetwork controller 860, which may be arranged to facilitatecommunications with one or more other computing devices 862 over anetwork communication link via one or more communication ports 864.

The network communication link may be one example of a communicationmedia. Communication media may typically be embodied by computerreadable instructions, data structures, program modules, or other datain a modulated data signal, such as a carrier wave or other transportmechanism, and may include any information delivery media. A “modulateddata signal” may be a signal that has one or more of its characteristicsset or changed in such a manner as to encode information in the signal.By way of example, and not limitation, communication media may includewired media such as a wired network or direct-wired connection, andwireless media such as acoustic, radio frequency (RF), microwave,infrared (IR) and other wireless media. The term computer readable mediaas used herein may include both storage media and communication media.

Computing device 800 may be implemented as a portion of a physicalserver, virtual server, a computing cloud, or a hybrid device that mayinclude any of the above functions. Computing device 800 may also beimplemented as a personal computer including both laptop computer andnon-laptop computer configurations. Moreover computing device 800 may beimplemented as a networked system or as part of a general purpose orspecialized server.

Networks for a networked system including computing device 800 maycomprise any topology of servers, clients, switches, routers, modems,Internet service providers, and any appropriate communication media(e.g., wired or wireless communications). A system according toembodiments may have a static or dynamic network topology. The networksmay include a secure network such as an enterprise network (e.g., a LAN,WAN, or WLAN), an unsecure network such as a wireless open network(e.g., IEEE 802.11 wireless networks), or a world-wide network such(e.g., the Internet). The networks may also comprise a plurality ofdistinct networks that may be adapted to operate together. Such networksmay be configured to provide communication between the nodes describedherein. By way of example, and not limitation, these networks mayinclude wireless media such as acoustic, RF, infrared and other wirelessmedia. Furthermore, the networks may be portions of the same network orseparate networks.

FIG. 9 illustrates a block diagram of an example computer programproduct that may be used to control the automated machine of FIG. 7 orsimilar manufacturing equipment in making an example perforated graphenemonolayer or example membrane thereof, arranged in accordance with atleast some embodiments described herein. In some examples, as shown inFIG. 9, computer program product 900 may include a signal bearing medium902 that may also include machine readable instructions 904 that, whenexecuted by, for example, a processor, may provide the functionalitydescribed above with respect to FIG. 6 through FIG. 8. For example,referring to processor 790, one or more of the tasks shown in FIG. 9 maybe undertaken in response to instructions 904 conveyed to the processor790 by medium 902 to perform actions associated with making an exampleperforated graphene monolayer or example membrane thereof as describedherein. Some of those instructions may include, for example, one or moreinstructions for: contacting R-Het* to a plurality of locations at agraphene monolayer; providing a separation distance between locations;reacting each R-Het* with at least one graphene carbon atom; forming aplurality of discrete pores in the graphene monolayer; and/or contactingthe perforated graphene monolayer to a permeable substrate.

In some implementations, signal bearing medium 902 depicted in FIG. 9may encompass a computer-readable medium 906, such as, but not limitedto, a hard disk drive, a Compact Disc (CD), a Digital Versatile Disk(DVD), a digital tape, memory, etc. In some implementations, signalbearing medium 902 may encompass a recordable medium 908, such as, butnot limited to, memory, read/write (R/W) CDs, R/W DVDs, etc. In someimplementations, signal bearing medium 902 may encompass acommunications medium 910, such as, but not limited to, a digital and/oran analog communication medium (e.g., a fiber optic cable, a waveguide,a wired communications link, a wireless communication link, etc.). Forexample, computer program product 900 may be conveyed to the processor904 by an RF signal bearing medium 902, where the signal bearing medium902 may be conveyed by a wireless communications medium 910 (e.g., awireless communications medium conforming with the IEEE 802.11standard). While the embodiments will be described in the generalcontext of program modules that execute in conjunction with anapplication program that runs on an operating system on a personalcomputer, those skilled in the art will recognize that aspects may alsobe implemented in combination with other program modules.

Generally, program modules may include routines, programs, components,data structures, and other types of structures that perform particulartasks or implement particular abstract data types. Moreover, thoseskilled in the art will appreciate that embodiments may be practicedwith other computer system configurations, including hand-held devices,multiprocessor systems, microprocessor-based or programmable consumerelectronics, minicomputers, mainframe computers, and comparablecomputing devices. Embodiments may also be practiced in distributedcomputing environments where tasks may be performed by remote processingdevices that may be linked through a communications network. In adistributed computing environment, program modules may be located inboth local and remote memory storage devices.

Embodiments may be implemented as a computer-implemented process(method), a computing system, or as an article of manufacture, such as acomputer program product or computer readable media. The computerprogram product may be a computer storage medium readable by a computersystem and encoding a computer program that comprises instructions forcausing a computer or computing system to perform example process(es).The computer-readable storage medium can for example be implemented viaone or more of a volatile computer memory, a non-volatile memory, a harddrive, a flash drive, a floppy disk, or a compact disk, and comparablemedia.

Throughout this specification, the term “platform” may be a combinationof software and hardware components for providing a configurationenvironment, which may facilitate configuration of software/hardwareproducts and services for a variety of purposes. Examples of platformsmay include, but are not limited to, a hosted service executed over aplurality of servers, an application executed on a single computingdevice, and comparable systems. The term “server” generally refers to acomputing device executing one or more software programs typically in anetworked environment. However, a server may also be implemented as avirtual server (software programs) executed on one or more computingdevices viewed as a server on the network. More detail on thesetechnologies and example operations is provided below.

An example membrane may include a graphene monolayer with a plurality ofdiscrete pores that are chemically perforated therein. Each of theplurality of discrete pores may have a substantially uniform pore sizecharacterized by one or more carbon vacancy defects in the graphenemonolayer such that the graphene monolayer may have substantiallyuniform pore sizes throughout.

In various examples, each of the plurality of discrete pores may becharacterized by at least about two carbon vacancy defects in thegraphene monolayer. In further examples, the graphene monolayer may becharacterized by a separation selectivity of: H₂ to CH₄ of at least200:1. In various examples, the plurality of discrete pores may becharacterized by a minimum separation of at least about 4 angstroms.

In some examples, the membrane may further include a permeable substratethat contacts the graphene monolayer, wherein the permeable substratemay include one or more of polyethylene, polypropylene, polyester,polyurethane, polystyrene, polyolefin, aramide, aromatic polyester,carbon fiber, polysulfone, polyethersulfone, a metal mesh, and/or porousceramic.

An example method may include contacting a compound represented byR-Het* to a plurality of locations at the graphene monolayer. Het* maybe nitrene or activated oxy. R may be one of —R^(a), —SO2R^(a),—(CO)OR^(a), or —SiR^(a)R^(b)R^(c). R^(a), R^(b), and R^(c) may beindependently aryl or heteroaryl. Some example methods may also includeproviding a separation distance of at least r_(R) between adjacentlocations in the plurality of locations, wherein r_(R) may be a minimumsteric radius of R. Various example methods may also include reactingthe compound represented by R-Het* with at least one graphene carbonatom C_(g) at each of the plurality of locations to form a plurality pof heteroatom-carbon moieties at the graphene monolayer represented by[R-Het-C_(g)]_(p)graphene. The method may also include forming aplurality of discrete pores in the graphene monolayer by removing aplurality of the heteroatom-carbon moieties represented by R-Het-C_(g),The plurality of discrete pores may be characterized by a plurality ofcarbon vacancy defects in the graphene monolayer defined by removing thegraphene carbon atoms C_(g) from the plurality of locations. Thegraphene monolayer may have substantially uniform pore sizes throughout.

In various examples, Het* may be nitrene; and each of the plurality ofheteroatom-carbon moieties at the graphene monolayer may be asubstituted aziridine represented by structural formula 502:

In some examples, the method may further include preparing R-Het* byreacting an azide precursor represented by R—N₃ under thermolytic orphotolytic conditions suitable for converting azide to nitrene, whereinHet* may be nitrene.

In further examples, the method may also include preparing R-Het* byreacting an azide precursor represented by R—N—OSO₂—R^(f) with a base,wherein R^(f) may be a mesylate, triflate, brosylate, tosylate ornosylate group, wherein Het* may be nitrene and R may be —(CO)OR^(a).

In various examples, the method may further include cleaving a pluralityof the R groups to produce a plurality of N—H aziridine moieties at thegraphene monolayer that may each be represented by structural formula504:

In some examples of the method, wherein R may be —SiR^(a)R^(b)R^(c) andthe plurality of R groups may be cleaved by contacting each substitutedaziridine represented by structural formula I with one of: a quaternaryammonium fluoride; an alkyl sulfonic acid; an aryl sulfonic acid;trifluoromethane sulfonic acid; an alkali metal hydroxide; or anoxidant.

In further examples of the method, wherein R may be —(CO)OR^(a) and theplurality of R groups may be cleaved by contacting each substitutedaziridine represented by structural formula I with one of: an alkalialkylthiolate; a trialkyl silyl iodide; an alkali metal hydroxide; analkali earth metal hydroxide; potassium carbonate; HBr/acetic acid;sodium bis(2-methoxyethoxy)aluminum hydride; sodium tellurium hydride; apotassium trialkylsiloxide; an alkyl lithium; a quaternary ammoniumfluoride; an acyl chloride with sodium iodide; an alkyl sulfonic acid;trifluoromethane sulfonic acid; or an aryl sulfonic acid.

In various examples of the method, wherein R may be —SO₂R^(a) and theplurality of R groups may be cleaved by contacting each substitutedaziridine represented by structural formula I with one of: HBr andacetic acid; HBr and phenol; HF and pyridine; sodiumbis(2-methoxyethoxy)aluminum hydride; an alkali metal arylide salt; analkali metal in ammonia or iso-propylamine; sodium-potassium alloyadsorbed on silica gel; samarium iodide; perchloric acid in acetic acid;photolysis in the presence of ether; photolysis in the presence ofsodium borohydride and dimethoxybenzene; photolysis in the presence ofhydrazine; photolysis in the presence of borane:ammonia; photolysis inthe presence of sodium borohydride and beta-naphthoxide; or sodiumamalgam in the presence of sodium monohydrogen phosphate.

In some examples, wherein R may be —R^(a), the plurality of R groups maybe cleaved by contacting each substituted aziridine represented bystructural formula I with one of: hydrogen in the presence of catalyticpalladium; borane in the presence of catalytic palladium; borane in thepresence of catalytic Raney nickel; or hydrogen peroxide followed bytetrasodium 5,10,15,20-tetra(4-sulfophenyl) porphyrinatoiron(II).

In further examples, the method may also include heating the pluralityof N—H aziridine moieties represented by structural formula 504 in thepresence of hydrogen gas to a temperature between about 750° C. andabout 900° C. to produce the plurality of pores in the graphenemonolayer as a plurality of single-carbon vacancy defects, that may eachbe represented by structural formula 506:

In various examples, the method may further include: hydrolyzing theplurality of N—H aziridine moieties represented by structural formula504 to produce a plurality of beta-amino alcohol moieties at thegraphene monolayer that may each be represented by structural formula508; and heating the plurality of N—H aziridine moieties represented bystructural formula 508 under hydrogen to a temperature between about750° C. and about 900° C. to produce the plurality of pores in thegraphene monolayer as a plurality of double-carbon vacancy defects thatmay each be represented by structural formula 510:

In some examples of the method, wherein: R may be —R^(a); Het* may beactivated oxy; and each of the plurality of heteroatom-carbon moietiesat the graphene monolayer may be a compound represented by structuralformula 512 or a compound represented by structural formula 518:

In further examples, the method may also include preparing R-Het* bycontacting a trivalent iodosoaryl reagent with one of: R^(a)—OH; analkaline metal salt of R^(a)—O⁻; an alkaline earth metal salt ofR^(a)—O⁻; R^(a)—CO₂H; an alkaline metal salt of R^(a)—CO₂ ⁻; or analkaline earth metal salt of R^(a)—CO₂ ⁻. In various examples, thetrivalent iodosoaryl reagent may be iodosobenzene tetrafluoroborate,iodosobenzene hexafluoroantimonate, or iodosobenzenehexafluorophosphate.

In some examples, the method may further include: reacting the compoundrepresented by structural formula 512 with one or more of hydrobromicacid, hydroiodic acid, boron tribromide, or aluminium trichloride; orreacting the compound represented by structural formula 518 with an acidor base, thereby forming a compound that may be represented bystructural formula 514:

In further examples, the method may also include: heating the compoundrepresented by structural formula 514 under hydrogen to a temperaturebetween about 750° C. and about 900° C. to produce the plurality ofpores in the graphene monolayer as a plurality of double-carbon vacancydefects that may each be represented by structural formula 510:

In various examples, the method may further include: contacting thegraphene monolayer with a permeable substrate, wherein the permeablesubstrate includes one or more of polyethylene, polypropylene,polyester, polyurethane, polystyrene, polyolefin, aramide, aromaticpolyester, carbon fiber, polysulfone, polyethersulfone, a metal mesh,and/or porous ceramic.

An example method of separating a compound from a fluid mixture mayinclude providing a fluid mixture that contains a first compound and asecond compound. Some example methods may also include providing amembrane that includes a graphene monolayer that may be chemicallyperforated by a plurality of discrete pores. Each of the plurality ofdiscrete pores may be characterized by one or more carbon vacancydefects such that the graphene monolayer has substantially uniform poresizes throughout. Each of the plurality of discrete pores may becharacterized by a diameter that may be selective for passage of thefirst compound compared to the second compound. Various example methodsmay also include contacting the fluid mixture to a first surface of thegraphene monolayer. Example methods may further include directing thefirst compound through the plurality of discrete pores to separate thefirst compound from the second compound.

In various examples of the method of separating a compound from a fluidmixture, the first compound may be smaller than the second molecule.

In some examples, the method of separating a compound from a fluidmixture may further include directing the first compound through theplurality of discrete pores by employing a gradient across the graphenemonolayer, wherein the gradient may be one or more of temperature,pressure, concentration, electric field, or electrochemical potential.

In further examples, the method of separating a compound from a fluidmixture may also include separating the first compound from the secondcompound at a separation selectivity of between about 200:1 and about10^23:1.

In various examples of the method of separating a compound from a fluidmixture, wherein the first compound may be one of helium, neon, argon,xenon, krypton, radon, hydrogen, nitrogen, oxygen, carbon monoxide,carbon dioxide, sulfur dioxide, hydrogen sulfide, a nitrogen oxide, aC1-C4 alkane, a silane, water, an organic solvent, or a haloacid.

The present disclosure also generally describes an example membrane. Anexample membrane may be prepared by a process that includes contacting acompound represented by R-Het* to a plurality of locations at a graphenemonolayer. Het* may be nitrene or activated oxy. R may be one of —R^(a),—SO2R^(a), —(CO)OR^(a), or —SiR^(a)R^(b)R^(c). R^(a), R^(b), and R^(c)may be independently aryl or heteroaryl. Some example membranes may beprepared by a process that also includes providing a separation distanceof at least r_(R) between adjacent locations in the plurality oflocations, wherein r_(R) may be a minimum steric radius of R. Theexample membrane may be prepared by a process that further includesreacting the compound represented by R-Her with at least one graphenecarbon atom C_(g) at each of the plurality of locations to form aplurality p of heteroatom-carbon moieties at the graphene monolayerrepresented by [R-Het-C_(g)]_(p)graphene. The example membrane may beprepared by a process that also includes forming a plurality of discretepores in the graphene monolayer by removing a plurality of theheteroatom-carbon moieties represented by R-Het-C_(g). The plurality ofdiscrete pores may be characterized by a plurality of carbon vacancydefects in the graphene monolayer defined by removing the graphenecarbon atoms C_(g) from the plurality of locations. The graphenemonolayer may have substantially uniform pore sizes throughout.

The present disclosure also generally describes system for preparing agraphene membrane with substantially uniform pores. The system mayinclude: a reagent activator for preparing an activated reagent from aprecursor reagent; a reagent applicator configured to contact theactivated reagent to a plurality of locations at a graphene monolayer; areaction chamber configured to hold the graphene monolayer; a heaterconfigured to thermally cleave a plurality of heteroatom-carbon moietiesat the graphene monolayer to form a perforated graphene monolayer; and asupport substrate applicator configured to contact the perforatedgraphene monolayer to a support substrate.

In various examples of the system, the reagent activator may include oneor more of: a resistive heating element; an infrared laser; anultraviolet light source; and/or a reaction chamber configured tocontact the precursor compound and a trivalent iodosoaryl compound.

In some examples of the system, the reagent applicator may include oneor more of: a solution coater; a spin coater; a dip coater; apressurized fluid applicator; a reagent reservoir; a vacuum chamber; acondenser; and/or a chemical vapor deposition chamber.

In further examples of the system, the heater may include one or moreof: a hydrogen source; a resistive heating element; and/or an infraredlaser.

In various examples of the system, the support substrate applicator mayinclude one or more of: a solution coater, a spin coater, a dip coater,a curing oven an ultraviolet light source an etching chamber, a washingchamber, and/or a contact press.

The terms “a” and “an” as used herein mean “one or more” unless thesingular is expressly specified. For example, reference to “a base” mayinclude a mixture of two or more bases, as well as a single base.

As used herein, “about” will be understood by persons of ordinary skillin the art and will vary to some extent depending upon the context inwhich “about” is used. If there are uses of the term which are not clearto persons of ordinary skill in the art, given the context in which theterm is used, “about” will mean up to, plus or minus 10% of theparticular term.

As used herein, the terms “optional” and “optionally” mean that thesubsequently described circumstance may or may not occur, so that thedescription may include instances where the circumstance occurs andinstances where it does not.

As used herein, “substituted” refers to an organic group as definedbelow (e.g., an alkyl group) in which one or more bonds to a hydrogenatom contained therein may be replaced by a bond to non-hydrogen ornon-carbon atoms. Groups not explicitly stated to be one of substitutedor unsubstituted may be either substituted or unsubstituted. Substitutedgroups also may include groups in which one or more bonds to a carbon(s)or hydrogen(s) atom may be replaced by one or more bonds, includingdouble or triple bonds, to a heteroatom. A substituted group may besubstituted with one or more substituents, unless otherwise specified.In some embodiments, a substituted group may be substituted with 1, 2,3, 4, 5, or 6 substituents. Examples of substituent groups may include:halogens (i.e., F, Cl, Br, and I); hydroxyls; alkoxy, alkenoxy, aryloxy,aralkyloxy, heterocyclyloxy, and heterocyclylalkoxy groups; carbonyls(oxo); carboxyls; esters; urethanes; oximes; hydroxylamines;alkoxyamines; aralkoxyamines; thiols; sulfides; sulfoxides; sulfones;sulfonyls; sulfonamides; amines; N-oxides; hydrazines; hydrazides;hydrazones; azides; amides; ureas; amidines; guanidines; enamines;imides; iso-cyanates; iso-thiocyanates; cyanates; thiocyanates; imines;nitro groups; nitriles (i.e., CN); and the like.

Substituted ring groups such as substituted cycloalkyl, aryl,heterocyclyl and heteroaryl groups also may include rings and ringsystems in which a bond to a hydrogen atom may be replaced with a bondto a carbon atom. Substituted cycloalkyl, aryl, heterocyclyl andheteroaryl groups may also be substituted with substituted orunsubstituted alkyl, alkenyl, and alkynyl groups as defined below.

Alkyl groups may include straight chain and branched chain alkyl groupshaving from 1 to 12 carbon atoms, and typically from 1 to 10 carbons or,in some examples, from 1 to 8, 1 to 6, or 1 to 4 carbon atoms. Examplesof straight chain alkyl groups may include groups such as methyl, ethyl,n-propyl, n-butyl, n-pentyl, n-hexyl, n-heptyl, and n-octyl groups.Examples of branched alkyl groups may include, but are not limited to,iso-propyl, iso-butyl, sec-butyl, tert-butyl, neopentyl, iso-pentyl, and2,2-dimethylpropyl groups. Representative substituted alkyl groups maybe substituted one or more times with substituents such as those listedabove and may include, without limitation, haloalkyl (e.g.,trifluoromethyl), hydroxyalkyl, thioalkyl, aminoalkyl, alkylaminoalkyl,dialkylaminoalkyl, alkoxyalkyl, carboxyalkyl, and the like.

Cycloalkyl groups may include mono-, bi- or tricyclic alkyl groupshaving from 3 to 12 carbon atoms in the ring(s), or, in someembodiments, 3 to 10, 3 to 8, or 3 to 4, 5, or 6 carbon atoms. Exemplarymonocyclic cycloalkyl groups may include, but are not limited to,cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl, cycloheptyl, andcyclooctyl groups. In some embodiments, the cycloalkyl group has 3 to 8ring members, whereas in other embodiments, the number of ring carbonatoms ranges from 3 to 5, 3 to 6, or 3 to 7. Bi- and tricyclic ringsystems may include both bridged cycloalkyl groups and fused rings, suchas, but not limited to, bicyclo[2.1.1]hexane, adamantyl, decalinyl, andthe like. Substituted cycloalkyl groups may be substituted one or moretimes with non-hydrogen and non-carbon groups as defined above. However,substituted cycloalkyl groups also may include rings that may besubstituted with straight or branched chain alkyl groups as definedabove. Representative substituted cycloalkyl groups may bemono-substituted or substituted more than once, such as, but not limitedto, 2,2-, 2,3-, 2,4-, 2,5- or 2,6-disubstituted cyclohexyl groups, whichmay be substituted with substituents such as those listed above.

Aryl groups may be cyclic aromatic hydrocarbons that do not containheteroatoms. Aryl groups herein may include monocyclic, bicyclic andtricyclic ring systems. Aryl groups may include, but are not limited to,phenyl, azulenyl, heptalenyl, biphenyl, fluorenyl, phenanthrenyl,anthracenyl, indenyl, indanyl, pentalenyl, and naphthyl groups. In someembodiments, aryl groups contain 6-14 carbons, and in others from 6 to12 or even 6-10 carbon atoms in the ring portions of the groups. In someembodiments, the aryl groups may be phenyl or naphthyl. “Aryl groups”may include groups containing fused rings, such as fusedaromatic-aliphatic ring systems (e.g., indanyl, tetrahydronaphthyl, andthe like). “Aryl groups”, unless explicitly stated to be one ofsubstituted or unsubstituted, may be either unsubstituted or substitutedwith other groups, such as alkyl or halo groups, bonded to one of thering members. Representative substituted aryl groups may bemono-substituted or substituted more than once. For example,monosubstituted aryl groups include, but are not limited to, 2-, 3-, 4-,5-, or 6-substituted phenyl or naphthyl groups, which may be substitutedwith substituents such as those listed above.

Aralkyl groups may be alkyl groups as defined above in which a hydrogenor carbon bond of an alkyl group may be replaced with a bond to an arylgroup as defined above. In some embodiments, aralkyl groups contain 7 to16 carbon atoms, 7 to 14 carbon atoms, or 7 to 10 carbon atoms.Substituted aralkyl groups may be substituted at the alkyl, the aryl orboth the alkyl and aryl portions of the group. Representative aralkylgroups may include but are not limited to benzyl and phenethyl groupsand fused (cycloalkylaryl)alkyl groups such as 4-indanylethyl.Representative substituted aralkyl groups may be substituted one or moretimes with substituents such as those listed above.

Heterocyclyl groups may include aromatic (also referred to asheteroaryl) and non-aromatic ring compounds containing 3 or more ringmembers of which one or more may be a heteroatom such as, but notlimited to, N, O, and S. In some embodiments, the heterocyclyl groupcontains 1, 2, 3 or 4 heteroatoms. In some embodiments, heterocyclylgroups may include mono-, bi- and tricyclic rings having 3 to 16 ringmembers, whereas other such groups have 3 to 6, 3 to 10, 3 to 12, or 3to 14 ring members. Heterocyclyl groups encompass aromatic, partiallyunsaturated and saturated ring systems, such as, for example,imidazolyl, imidazolinyl and imidazolidinyl groups. The phrase“heterocyclyl group” may include fused ring species including thosecomprising fused aromatic and non-aromatic groups, such as, for example,benzotriazolyl, 2,3-dihydrobenzo[1,4]dioxinyl, and benzo[1,3]dioxolyl.“Heterocyclyl group” also may include bridged polycyclic ring systemscontaining a heteroatom such as, but not limited to, quinuclidyl. A“Heterocyclyl group”, unless explicitly stated to be one of substitutedor unsubstituted, may be either unsubstituted or substituted with othergroups, such as alkyl, oxo or halo groups, bonded to one of the ringmembers. Heterocyclyl groups may include, but are not limited to,aziridinyl, azetidinyl, pyrrolidinyl, imidazolidinyl, pyrazolidinyl,thiazolidinyl, tetrahydrothiophenyl, tetrahydrofuranyl, dioxolyl,furanyl, thiophenyl, pyrrolyl, pyrrolinyl, imidazolyl, imidazolinyl,pyrazolyl, pyrazolinyl, triazolyl, tetrazolyl, oxazolyl, iso-xazolyl,thiazolyl, thiazolinyl, iso-thiazolyl, thiadiazolyl, oxadiazolyl,piperidyl, piperazinyl, morpholinyl, thiomorpholinyl, tetrahydropyranyl,tetrahydrothiopyranyl, oxathiane, dioxyl, dithianyl, pyranyl, pyridyl,pyrimidinyl, pyridazinyl, pyrazinyl, triazinyl, dihydropyridyl,dihydrodithiinyl, dihydrodithionyl, homopiperazinyl, quinuclidyl,indolyl, indolinyl, iso-indolyl, azaindolyl (pyrrolopyridyl), indazolyl,indolizinyl, benzotriazolyl, benzimidazolyl, benzofuranyl,benzothiophenyl, benzthiazolyl, benzoxadiazolyl, benzoxazinyl,benzodithiinyl, benzoxathiinyl, benzothiazinyl, benzoxazolyl,benzothiazolyl, benzothiadiazolyl, benzo[1,3]dioxolyl, pyrazolopyridyl,imidazopyridyl (azabenzimidazolyl), triazolopyridyl, iso-xazolopyridyl,purinyl, xanthinyl, adeninyl, guaninyl, quinolinyl, iso-quinolinyl,quinolizinyl, quinoxalinyl, quinazolinyl, cinnolinyl, phthalazinyl,naphthyridinyl, pteridinyl, thianaphthyl, dihydrobenzothiazinyl,dihydrobenzofuranyl, dihydroindolyl, dihydrobenzodioxinyl,tetrahydroindolyl, tetrahydroindazolyl, tetrahydrobenzimidazolyl,tetrahydrobenzotriazolyl, tetrahydropyrrolopyridyl,tetrahydropyrazolopyridyl, tetrahydroimidazopyridyl,tetrahydrotriazolopyridyl, and tetrahydroquinolinyl groups.Representative substituted heterocyclyl groups may be mono-substitutedor substituted more than once, such as, but not limited to, pyridyl ormorpholinyl groups, which may be 2-, 3-, 4-, 5-, or 6-substituted, ordisubstituted with various substituents such as those listed above.

Heteroaryl groups may be aromatic ring compounds containing 5 or morering members, of which one or more may be a heteroatom such as, but notlimited to, N, O, and S. Heteroaryl groups include, but are not limitedto, groups such as pyrrolyl, pyrazolyl, triazolyl, tetrazolyl, oxazolyl,iso-xazolyl, thiazolyl, pyridinyl, pyridazinyl, pyrimidinyl, pyrazinyl,thiophenyl, benzothiophenyl, furanyl, benzofuranyl, indolyl, azaindolyl(pyrrolopyridinyl), indazolyl, benzimidazolyl, imidazopyridinyl(azabenzimidazolyl), pyrazolopyridinyl, triazolopyridinyl,benzotriazolyl, benzoxazolyl, benzothiazolyl, benzothiadiazolyl,imidazopyridinyl, iso-xazolopyridinyl, thianaphthyl, purinyl, xanthinyl,adeninyl, guaninyl, quinolinyl, iso-quinolinyl, tetrahydroquinolinyl,quinoxalinyl, and quinazolinyl groups. Heteroaryl groups include fusedring compounds in which rings may be aromatic such as indolyl groups andinclude fused ring compounds in which only one of the rings may bearomatic, such as 2,3-dihydro indolyl groups. “Heteroaryl groups” mayinclude fused ring compounds. “Heteroaryl groups” unless explicitlystated to be substituted or to be unsubstituted, may be eitherunsubstituted or substituted with other groups bonded to one of the ringmembers, such as alkyl groups. Representative substituted heteroarylgroups may be substituted one or more times with various substituentssuch as those listed above.

Heteroaralkyl groups may be alkyl groups as defined above in which ahydrogen or carbon bond of an alkyl group may be replaced with a bond toa heteroaryl group as defined above. Substituted heteroaralkyl groupsmay be substituted at the alkyl, the heteroaryl or both the alkyl andheteroaryl portions of the group. Representative substitutedheteroaralkyl groups may be substituted one or more times withsubstituents such as those listed above.

Groups described herein having two or more points of attachment (i.e.,divalent, trivalent, or polyvalent) within the compound of thetechnology may be designated by use of the suffix, “ene.” For example,divalent alkyl groups may be alkylene groups, divalent aryl groups maybe arylene groups, divalent heteroaryl groups may be heteroarylenegroups, and so forth.

Alkoxy groups may be hydroxyl groups (—OH) in which the bond to thehydrogen atom may be replaced by a bond to a carbon atom of asubstituted or unsubstituted alkyl group as defined above. Examples oflinear alkoxy groups include, but are not limited to, methoxy, ethoxy,propoxy, butoxy, pentoxy, hexoxy, and the like. Examples of branchedalkoxy groups include, but are not limited to, iso-propoxy, sec-butoxy,tert-butoxy, iso-pentoxy, iso-hexoxy, and the like. Examples ofcycloalkoxy groups include, but are not limited to, cyclopropyloxy,cyclobutyloxy, cyclopentyloxy, cyclohexyloxy, and the like.Representative substituted alkoxy groups may be substituted one or moretimes with substituents such as those listed above.

The term “amine” (or “amino”), as used herein, refers to NR₅R₆ groups,wherein R₅ and R₆ may be independently hydrogen, or a substituted orunsubstituted alkyl, alkenyl, alkynyl, cycloalkyl, aryl, aralkyl,heterocyclylalkyl or heterocyclyl group as defined herein. In someembodiments, the amine may be alkylamino, dialkylamino, arylamino, oralkylarylamino. In other embodiments, the amine may be NH₂, methylamino,dimethylamino, ethylamino, diethylamino, propylamino, iso-propylamino,phenylamino, or benzylamino. The term “alkylamino” may be defined asNR₇R₈, wherein at least one of R₇ and R₈ may be alkyl and the other maybe alkyl or hydrogen. The term “arylamino” may be defined as NR₉R₁₀,wherein at least one of R₉ and R₁₀ may be aryl and the other may be arylor hydrogen.

The term “halogen” or “halo,” as used herein, refers to bromine,chlorine, fluorine, or iodine. In some embodiments, the halogen may befluorine. In other embodiments, the halogen may be chlorine or bromine.

There is little distinction left between hardware and softwareimplementations of aspects of systems; the use of hardware or softwareis generally (but not always, in that in certain contexts the choicebetween hardware and software may become significant) a design choicerepresenting cost vs. efficiency tradeoffs. There are various vehiclesby which processes and/or systems and/or other technologies describedherein may be effected (e.g., hardware, software, and/or firmware), andthat the preferred vehicle will vary with the context in which theprocesses and/or systems and/or other technologies are deployed. Forexample, if an implementer determines that speed and accuracy areparamount, the implementer may opt for a mainly hardware and/or firmwarevehicle; if flexibility is paramount, the implementer may opt for amainly software implementation; or, yet again alternatively, theimplementer may opt for some combination of hardware, software, and/orfirmware.

The foregoing detailed description has set forth various embodiments ofthe devices and/or processes via the use of block diagrams, flowcharts,and/or examples. Insofar as such block diagrams, flowcharts, and/orexamples contain one or more functions and/or operations, it will beunderstood by those within the art that each function and/or operationwithin such block diagrams, flowcharts, or examples may be implemented,individually and/or collectively, by a wide range of hardware, software,firmware, or virtually any combination thereof. In one embodiment,several portions of the subject matter described herein may beimplemented via Application Specific Integrated Circuits (ASICs), FieldProgrammable Gate Arrays (FPGAs), digital signal processors (DSPs), orother integrated formats. However, those skilled in the art willrecognize that some aspects of the embodiments disclosed herein, inwhole or in part, may be equivalently implemented in integratedcircuits, as one or more computer programs running on one or morecomputers (e.g., as one or more programs running on one or more computersystems), as one or more programs running on one or more processors(e.g. as one or more programs running on one or more microprocessors),as firmware, or as virtually any combination thereof, and that designingthe circuitry and/or writing the code for the software and or firmwarewould be well within the skill of one of skill in the art in light ofthis disclosure.

The present disclosure is not to be limited in terms of the particularembodiments described in this application, which are intended asillustrations of various aspects. Many modifications and variations maybe made without departing from its spirit and scope, as will be apparentto those skilled in the art. Functionally equivalent methods andapparatuses within the scope of the disclosure, in addition to thoseenumerated herein, will be apparent to those skilled in the art from theforegoing descriptions. Such modifications and variations are intendedto fall within the scope of the appended claims. The present disclosureis to be limited only by the terms of the appended claims, along withthe full scope of equivalents to which such claims are entitled. It isto be understood that this disclosure is not limited to particularmethods, systems, or components, which can, of course, vary. It is alsoto be understood that the terminology used herein is for the purpose ofdescribing particular embodiments only, and is not intended to belimiting.

In addition, those skilled in the art will appreciate that themechanisms of the subject matter described herein are capable of beingdistributed as a program product in a variety of forms, and that anillustrative embodiment of the subject matter described herein appliesregardless of the particular type of signal bearing medium used toactually carry out the distribution. Examples of a signal bearing mediuminclude, but are not limited to, the following: a recordable type mediumsuch as a floppy disk, a hard disk drive, a Compact Disc (CD), a DigitalVersatile Disk (DVD), a digital tape, a computer memory, etc.; and atransmission type medium such as a digital and/or an analogcommunication medium (e.g., a fiber optic cable, a waveguide, a wiredcommunications link, a wireless communication link, etc.).

Those skilled in the art will recognize that it is common within the artto describe devices and/or processes in the fashion set forth herein,and thereafter use engineering practices to integrate such describeddevices and/or processes into data processing systems. That is, at leasta portion of the devices and/or processes described herein may beintegrated into a data processing system via a reasonable amount ofexperimentation. Those having skill in the art will recognize that atypical data processing system generally includes one or more of asystem unit housing, a video display device, a memory such as volatileand non-volatile memory, processors such as microprocessors and digitalsignal processors, computational entities such as operating systems,drivers, graphical user interfaces, and applications programs, one ormore interaction devices, such as a touch pad or screen, and/or controlsystems including feedback loops.

A typical manufacturing system may be implemented utilizing any suitablecommercially available components, such as those typically found in datacomputing/communication and/or network computing/communication systems.The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, different othercomponents. It is to be understood that such depicted architectures aremerely exemplary, and that in fact many other architectures may beimplemented which achieve the same functionality. In a conceptual sense,any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality may be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermediate components. Likewise, any two componentsso associated may also be viewed as being “operably connected”, or“operably coupled”, to each other to achieve the desired functionality,and any two components capable of being so associated may also be viewedas being “operably couplable”, to each other to achieve the desiredfunctionality. Specific examples of operably couplable include but arenot limited to physically connectable and/or physically interactingcomponents and/or wirelessly interactable and/or wirelessly interactingcomponents and/or logically interacting and/or logically interactablecomponents.

With respect to the use of substantially any plural and/or singularterms herein, those having skill in the art can translate from theplural to the singular and/or from the singular to the plural as isappropriate to the context and/or application. The varioussingular/plural permutations may be expressly set forth herein for sakeof clarity.

It will be understood by those within the art that, in general, termsused herein, and especially in the appended claims (e.g., bodies of theappended claims) are generally intended as “open” terms (e.g., the term“including” should be interpreted as “including but not limited to,” theterm “having” should be interpreted as “having at least,” the term“includes” should be interpreted as “includes but is not limited to,”etc.). It will be further understood by those within the art that if aspecific number of an introduced claim recitation is intended, such anintent will be explicitly recited in the claim, and in the absence ofsuch recitation no such intent is present. For example, as an aid tounderstanding, the following appended claims may contain usage of theintroductory phrases “at least one” and “one or more” to introduce claimrecitations. However, the use of such phrases should not be construed toimply that the introduction of a claim recitation by the indefinitearticles “a” or “an” limits any particular claim containing suchintroduced claim recitation to embodiments containing only one suchrecitation, even when the same claim includes the introductory phrases“one or more” or “at least one” and indefinite articles such as “a” or“an” (e.g., “a” and/or “an” should be interpreted to mean “at least one”or “one or more”); the same holds true for the use of definite articlesused to introduce claim recitations. In addition, even if a specificnumber of an introduced claim recitation is explicitly recited, thoseskilled in the art will recognize that such recitation should beinterpreted to mean at least the recited number (e.g., the barerecitation of “two recitations,” without other modifiers, means at leasttwo recitations, or two or more recitations).

Furthermore, in those instances where a convention analogous to “atleast one of A, B, and C, etc.” is used, in general such a constructionis intended in the sense one having skill in the art would understandthe convention (e.g., “a system having at least one of A, B, and C”would include but not be limited to systems that have A alone, B alone,C alone, A and B together, A and C together, B and C together, and/or A,B, and C together, etc.). In those instances where a conventionanalogous to “at least one of A, B, or C, etc.” is used, in general sucha construction is intended in the sense one having skill in the artwould understand the convention (e.g., “a system having at least one ofA, B, or C” would include but not be limited to systems that have Aalone, B alone, C alone, A and B together, A and C together, B and Ctogether, and/or A, B, and C together, etc.). It will be furtherunderstood by those within the art that virtually any disjunctive wordand/or phrase presenting two or more alternative terms, whether in thedescription, claims, or drawings, should be understood to contemplatethe possibilities of including one of the terms, either of the terms, orboth terms. For example, the phrase “A or B” will be understood toinclude the possibilities of “A” or “B” or “A and B.”

In addition, where features or aspects of the disclosure are describedin terms of Markush groups, those skilled in the art will recognize thatthe disclosure is also thereby described in terms of any individualmember or subgroup of members of the Markush group. As will beunderstood by one skilled in the art, for any and all purposes, such asin terms of providing a written description, all ranges disclosed hereinalso encompass any and all possible sub-ranges and combinations ofsub-ranges thereof. Any listed range can be easily recognized assufficiently describing and enabling the same range being broken downinto at least equal halves, thirds, quarters, fifths, tenths, etc. As anon-limiting example, each range discussed herein can be readily brokendown into a lower third, middle third and upper third, etc. As will alsobe understood by one skilled in the art all language such as “up to,”“at least,” “greater than,” “less than,” and the like include the numberrecited and refer to ranges which can be subsequently broken down intosub-ranges as discussed above. Finally, as will be understood by oneskilled in the art, a range includes each individual member. Forexample, a group having 1-3 cells refers to groups having 1, 2, or 3cells. Similarly, a group having 1-5 cells refers to groups having 1, 2,3, 4, or 5 cells, and so forth. While various aspects and embodimentshave been disclosed herein, other aspects and embodiments will beapparent to those skilled in the art.

The various aspects and embodiments disclosed herein are for purposes ofillustration and are not intended to be limiting, with the true scopeand spirit being indicated by the following claims.

What is claimed is:
 1. A membrane, comprising: a graphene monolayerincluding a plurality of discrete pores that are chemically perforatedtherein, each of the plurality of discrete pores having a substantiallyuniform pore size characterized by one or more carbon vacancy defects inthe graphene monolayer such that the graphene monolayer hassubstantially uniform pore sizes throughout; and a permeable substratearranged to contact the graphene monolayer, wherein the permeablesubstrate includes one or more of a polymer, a metal mesh, and/or porousceramic.
 2. The membrane of claim 1, wherein each of the plurality ofdiscrete pores is characterized by at least two carbon vacancy defectsin the graphene monolayer.
 3. The membrane of claim 1, wherein thegraphene monolayer is characterized by a separation selectivity of:H₂:CH₄ of at least 200:1.
 4. The membrane of claim 1, wherein theplurality of discrete pores is characterized by a minimum separation ofat least about 4 angstroms.
 5. The membrane of claim 1, wherein thepolymer is one or more of polyethylene, polypropylene, polyester,polyurethane, polystyrene, polyolefin, aramide, aromatic polyester,carbon fiber, polysulfone, and/or polyethersulfone.
 6. A method to forma plurality of discrete pores in a graphene monolayer, comprising:contacting a compound represented by R-Het* to a plurality of locationsat the graphene monolayer, wherein: Het* is nitrene or activated oxy; Ris one of —R^(a), —SO₂R^(a), —(CO)OR^(a), or —SiR^(a)R^(b)R^(c); andR^(a), R^(b), and R^(c) are independently aryl or heteroaryl; providinga separation distance of at least r_(R) between adjacent locations inthe plurality of locations, wherein r_(R) is a minimum steric radius ofR; reacting the compound represented by R-Het* with at least onegraphene carbon atom C_(g) at each of the plurality of locations to forma plurality p of heteroatom-carbon moieties at the graphene monolayer tomodify the graphene monolayer, wherein the modified graphene monolayeris represented by [R-Het-C_(g)]_(p)graphene; and forming a plurality ofdiscrete pores in the graphene monolayer by removing the plurality p ofheteroatom-carbon moieties represented by R-Het-C_(g), wherein theplurality of discrete pores is characterized by a plurality of carbonvacancy defects in the graphene monolayer defined by removing the atleast one graphene carbon atomC_(g) from the plurality of locations suchthat the graphene monolayer has substantially uniform pore sizesthroughout.
 7. The method of claim 6, wherein: Het* is nitrene; and eachof the plurality p of heteroatom-carbon moieties at the graphenemonolayer is a substituted aziridine represented by a structuralformula:


8. The method of claim 7, further comprising preparing R-Het* by one of:reacting an azide precursor represented by R—N₃ under thermolytic orphotolytic conditions suitable to convert azide to nitrene; or reactingan azide precursor represented by R—N—OSO₂—R^(f) with a base, whereinR^(f) is a mesylate, triflate, brosylate, tosylate or nosylate group andR is —(CO)OR^(a).
 9. The method of claim 7, further comprising cleavinga plurality of R groups to produce a plurality of N—H aziridine moietiesat the graphene monolayer, each of the plurality of N—H aziridinemoieties represented by a structural formula:

wherein R is one of: —SiR^(a)R^(b)R^(c) and the plurality of R groups iscleaved by contacting each substituted aziridine represented by thestructural formula I

with one of: a quaternary ammonium fluoride; an alkyl sulfonic acid; anaryl sulfonic acid; trifluoromethane sulfonic acid; an alkali metalhydroxide; or an oxidant; —(CO)OR^(a) and the plurality of R groups iscleaved by contacting each substituted aziridine represented by thestructural formula

with one of: an alkali alkylthiolate; a trialkyl silyl iodide; an alkalimetal hydroxide; an alkali earth metal hydroxide; potassium carbonate;HBr/acetic acid; sodium bis(2-methoxyethoxy)aluminum hydride; sodiumtellurium hydride; a potassium trialkylsiloxide; an alkyl lithium; aquaternary ammonium fluoride; an acyl chloride with sodium iodide; analkyl sulfonic acid; trifluoromethane sulfonic acid; or an aryl sulfonicacid; —SO₂R^(a) and the plurality of R groups is cleaved by contactingeach substituted aziridine represented by the structural formula

with one of: HBr and acetic acid; HBr and phenol; HF and pyridine;sodium bis(2-methoxyethoxy)aluminum hydride; an alkali metal arylidesalt; an alkali metal in ammonia or iso-propylamine; sodium-potassiumalloy adsorbed on silica gel; samarium iodide; perchloric acid in aceticacid; photolysis in presence of ether; photolysis in presence of sodiumborohydride and dimethoxybenzene; photolysis in presence of hydrazine;photolysis in presence of borane:ammonia; photolysis in presence ofsodium borohydride and beta-naphthoxide; or sodium amalgam in presenceof sodium monohydrogen phosphate; or —R^(a) and the plurality of Rgroups is cleaved by contacting each substituted aziridine representedby the structural formula

with one of: hydrogen in presence of catalytic palladium; borane inpresence of catalytic palladium; borane in presence of catalytic Raneynickel; or hydrogen peroxide followed by tetrasodium5,10,15,20-tetra(4-sulfophenyl)porphyrinatoiron(II).
 10. The method ofclaim 9, further comprising heating the plurality of N—H aziridinemoieties represented by the structural formula

in presence of hydrogen gas to a temperature between about 750° C. andabout 900° C. to produce the plurality of pores in the graphenemonolayer as a plurality of single-carbon vacancy defects, each of theplurality of single-carbon vacancy defects represented by a structuralformula:


11. The method of claim 9, further comprising: hydrolyzing the pluralityof N—H aziridine moieties represented by the structural formula

to produce a plurality of beta-amino alcohol moieties at the graphenemonolayer, each of the plurality of beta-amino alcohol moietiesrepresented by a structural formula:

and heating the plurality of N—H aziridine moieties represented by thestructural formula

under hydrogen to a temperature between about 750° C. and about 900° C.to produce the plurality of pores in the graphene monolayer as aplurality of double-carbon vacancy defects, each of the plurality ofdouble-carbon vacancy defects represented by a structural formula:


12. The method of claim 6, wherein: R is —R^(a); Het* is activated oxy;and each of the plurality p of heteroatom-carbon moieties at thegraphene monolayer is a compound represented by a structural formula:

or a compound represented by a structural formula:


13. The method of claim 12, further comprising preparing R-Het* bycontacting a trivalent iodosoaryl reagent with one of: R^(a)—OH; analkaline metal salt of R^(a)—O⁻; an alkaline earth metal salt ofR^(a)—O⁻; R^(a)—CO₂H; an alkaline metal salt of R^(a)—CO₂ ⁻; or analkaline earth metal salt of R^(a)—CO₂ ⁻; wherein the trivalentiodosoaryl reagent is iodosobenzene tetrafluoroborate, iodosobenzenehexafluoroantimonate, or iodosobenzene hexafluorophosphate.
 14. Themethod of claim 12, further comprising one of: reacting the compoundrepresented by the structural formula

with one or more of hydrobromic acid, hydroiodic acid, boron tribromide,or aluminium trichloride; or reacting the compound represented by thestructural formula

with an acid or base, thereby forming a compound represented by astructural formula:


15. The method of claim 14, further comprising heating the compoundrepresented by the structural formula

under hydrogen to a temperature between about 750° C. and about 900° C.to produce the plurality of pores in the graphene monolayer as aplurality of double-carbon vacancy defects, each of the plurality ofdouble-carbon vacancy defects represented by the structural formula:


16. The method of claim 6, further comprising contacting the graphenemonolayer with a permeable substrate, wherein the permeable substrateincludes one or more of polyethylene, polypropylene, polyester,polyurethane, polystyrene, polyolefin, aramide, aromatic polyester,carbon fiber, polysulfone, polyethersulfone, a metal mesh, and/or porousceramic.
 17. A method to separate a compound from a fluid mixture,comprising: providing a fluid mixture that contains a first compound anda second compound; providing a membrane that includes a graphenemonolayer that is chemically perforated by a plurality of discretepores, wherein: each of the plurality of discrete pores is characterizedby one or more carbon vacancy defects such that the graphene monolayerhas substantially uniform pore sizes throughout, and each of theplurality of discrete pores is characterized by a diameter that isselective for passage of the first compound compared to the secondcompound; contacting the fluid mixture to a first surface of thegraphene monolayer; and directing the first compound through theplurality of discrete pores to separate the first compound from thesecond compound.
 18. The method of claim 17, wherein directing the firstcompound through the plurality of discrete pores includes directing thefirst compound through the plurality of discrete pores by employing agradient across the graphene monolayer, wherein the gradient is one ormore of temperature, pressure, concentration, electric field, orelectrochemical potential.
 19. The method of claim 17, whereinseparation of the first compound from the second compound includesseparating the first compound from the second compound at a separationselectivity of between about 200:1 and about 10^23:1.
 20. The method ofclaim 17, wherein the first compound is one of helium, neon, argon,xenon, krypton, radon, hydrogen, nitrogen, oxygen, carbon monoxide,carbon dioxide, sulfur dioxide, hydrogen sulfide, a nitrogen oxide, aC1-C4 alkane, a silane, water, an organic solvent, or a haloacid.
 21. Asystem to prepare a graphene membrane with substantially uniform pores,the system comprising: a reagent activator configured to prepare anactivated reagent from a precursor compound; a reagent applicatorconfigured to contact the activated reagent to a plurality of locationsat a graphene monolayer; a reaction chamber configured to hold thegraphene monolayer; a heater configured to thermally cleave a pluralityof heteroatom-carbon moieties at the graphene monolayer to form aperforated graphene monolayer; and a support substrate applicatorconfigured to contact the perforated graphene monolayer to a supportsubstrate.
 22. The system of claim 21, wherein: the reagent activatorincludes one or more of: a resistive heating element; an infrared laser;an ultraviolet light source; and/or a reaction chamber configured tocontact the precursor compound and a trivalent iodosoaryl compound; thereagent applicator includes one or more of: a solution coater; a spincoater; a dip coater; a pressurized fluid applicator; a reagentreservoir; a vacuum chamber; a condenser; and/or a chemical vapordeposition chamber; the heater includes one or more of: a reactionchamber configured to apply one of a partial pressure and flow ofhydrogen; a resistive heating element; and/or an infrared laser; and thesupport substrate applicator includes one or more of: a solution coater,a spin coater, a dip coater, a curing oven an ultraviolet light sourcean etching chamber, a washing chamber, and/or a contact press.